Her period will end when she is on her way to Makkah but she cannot do ghusl
Question

                If I am going to go for ‘umrah in Ramadan by bus, with an organised group, and I am menstruating, and my period ends when I am on the road, is it permissible for me to do tayammum for prayer until I reach the miqaat?

Because it is difficult to do ghusl in the washrooms on the road, because they are not sanitary and do not have any hot water, and I cannot hold up the group, because it is so crowded at the washrooms.

If it is permissible to do tayammum, can I pray with tayammum or should I do wudoo’ too? Should I do tayammum for every prayer or in the case of minor impurity?

When I reach Makkah, is it permissible for me to pray Taraweeh before doing ‘umrah, and to delay ‘umrah until there is less crowding?
Praise be to Allah.
    Firstly: 

    If a menstruating woman’s period 
    ends (and she becomes pure) when she is on the road, and there is still lots 
    of time left for the prayer, such as if her period ends before Zuhr, or 
    after it, then she may put Zuhr and ‘Asr together at the time of the later 
    prayer, and pray them at the time of ‘Asr, and she may delay her ghusl until 
    that time. Similarly, if her period ends after Maghrib, then she may pray 
    Maghrib and ‘Isha’ (together) at the time of ‘Isha’, and delay her ghusl 
    until the time of the prayer. 

    But if it is not possible to 
    delay the prayer, such as if her period ends shortly before Fajr or 
    afterwards, or before sunset, then in that case she must do ghusl so that 
    she can pray. 

    If she cannot find water, or she 
    can find it but is afraid to use it, because it is very cold and she has no 
    means of heating it, or she is afraid that her travelling companions will 
    move on, it is permissible for her to do tayammum. 

    It says in Mataalib Ooli an-Nuha 
    (1/194), concerning the excuses that make it permissible to do tayammum:

    Or he is afraid – if he uses the 
    water – of some physical harm such as an injury, or because it is very cold 
    and he cannot find anything with which to heat the water, or he is afraid 
    that if he uses it his travelling companions will move on. It says in al-Furoo‘: 
    The apparent meaning is that if he is not afraid of harm resulting from his 
    travelling companions moving on, because he will miss out on their company. 
    End quote. 

    But in the case of a slight 
    delay which will not adversely affect the group, then this does not matter 
    and is not an excuse for not doing ghusl. You have to fear Allah, may He be 
    exalted, and understand that the basic principle is that you should use 
    water, and that tayammum is only permissible when there is an excuse, so you 
    should not be too careless about that. 

    In the event that the concession 
    of tayammum is valid in your case, then if you do tayammum with the 
    intention of purifying yourself from both menses and minor impurity, you do 
    not need to do wudoo’ after tayammum. But if you do tayammum to purify 
    yourself from menses only, then you must do wudoo’ after that, and that is 
    preferable, in sha Allah, because water is available and you will not be 
    harmed by doing wudoo’ with it. 

    Shaykh ‘Abd al-‘Azeez ibn Baaz 
    (may Allah have mercy on him) was asked: 

    If a person falls asleep in Mina 
    and needs water for ghusl, but because of the high numbers of pilgrims there 
    is little water, what should he do instead of using water? What if he wants 
    to pray when he is junub? Is it acceptable for him to purify himself with 
    dust? I hope that you can explain this matter, because many people are faced 
    with such issues. 

    He (may Allah have mercy on him) 
    replied: 

    If a person has a wet dream in 
    Muzdalifah or any place where there are a lot of people, he should look for 
    water, even if he has to pay for it, from any place he can, on the edges of 
    Mina in any direction, or if he finds a place where he can do ghusl for 
    free, then he must do that. 

    But if that is not possible, 
    whether in return for payment or for free, and he cannot find any place to 
    do ghusl, then he must do tayammum with dust and pray. He should strike the 
    dust with his hands and wipe his face and hands with the intention of 
    purifying himself from janaabah and from minor impurity. In other words, he 
    should intend the tayammum to purify himself from both, the minor impurity 
    which necessitated wudoo’ and the major impurity which necessitated ghusl 
    from janaabah. He should intend both, and that will suffice, then he may 
    pray, and his prayer is valid, praise be to Allah. Fear Allah as much as you 
    can, for Allah says (interpretation of the meaning): “and you find no 
    water, perform Tayammum with clean earth and rub therewith your faces and 
    hands (Tayammum)” [an- Nisa’ 
    4:43]. 
    But he has to try hard and not be careless; he has to try hard and ask. If 
    he finds water, even if he has to pay for it and collect it in a bucket and 
    the like, he should do that, then move away from people, and look for a 
    tent, if there is a tent in which there is no one, or a place where no one 
    can see him, and do ghusl.

    End quote from Fataawa Noor 
    ‘ala ad-Darb by Shaykh Ibn Baaz (may Allah have mercy on him), (5/276). 
     

    Secondly: 

    With regard to your question 
    about tayammum and whether it is to be done for every prayer or, if it is 
    done to remove minor impurity once, that is sufficient. The scholars 
    differed concerning that as there are two views: 

    The first view is that it is not 
    required for every prayer, because tayammum – like wudoo’ – removes 
    impurity, so it is not invalidated by the ending of the time for the prayer; 
    rather it is invalidated by the things that are well-known to invalidate 
    wudoo’. 

    This is the view of the Hanafis 
    and is the view favoured by Shaykh al-Islam Ibn Taymiyah (may Allah have 
    mercy on him). It was regarded as more correct by Shaykh Ibn ‘Uthaymeen (may 
    Allah have mercy on him) – ash-Sharh al-Mumti‘ (1/314) 

    They quoted several things as 
    evidence, including the verse in which Allah, may He be exalted, says 
    (interpretation of the meaning):

    “If you are in a state of 
    Janaba (i.e. had a sexual discharge), purify yourself (bathe your whole 
    body). But if you are ill or on a journey or any of you comes from answering 
    the call of nature, or you have been in contact with women (i.e. sexual 
    intercourse) and you find no water, then perform Tayammum with clean earth 
    and rub therewith your faces and hands. Allah does not want to place you in 
    difficulty, but He wants to purify you”

    [al-Maa’idah 5:6]. 

    And the Prophet (blessings and 
    peace of Allah be upon him) said: “The earth has been made a place of 
    prostration and a means of purification for me.” (Agreed upon). Tayammum has 
    been ordained as a means of purification, so how can it be said that it does 
    not purify or that it does not remove impurity? Rather it is only a means to 
    make it permissible to pray. 

    The second scholarly view is: 

    That tayammum makes it 
    permissible to pray and so on, but it does not remove impurity. This is the 
    view of the majority of Maalikis, Shaafa‘is and Hanbalis. Based on that, 
    tayammum should be done after the time for the prayer begins, and it becomes 
    invalid when the time for the prayer ends. So if a person does tayammum for 
    Zuhr prayer, he may offer that prayer and whatever he wants of naafil 
    prayers, but when the time for Zuhr ends, he must do tayammum again for ‘Asr 
    prayer. 

    Undoubtedly it is preferable to 
    be on the safe side with regard to such matters, especially when there is no 
    hardship involved in doing tayammum for every prayer. 

    When you reach Makkah, it is 
    permissible for you to pray Taraweeh first, and to delay ‘umrah until a time 
    when the crowds are less, or to delay it so that you can rest and regain 
    strength and energy, so long as you avoid the things that are prohibited 
    when in ihram. 

    And Allah knows best.