What is the next meditation type after Mindfulness of Breathing meditation? I have been meditation using Mindfulness of Breathing mediation. I will continue for a while, while increasing the duration. 

When can I say that I "master" a type of meditation?

Are there a natural next type of meditation after Mindfulness of Breathing?
Meditation should be perceived as a tool to achieve some goal. We don't meditate to be good at meditation, rather, we use it because we want some results.

Buddhist practice is based on three pillars - Right View, Meditation and Action. We need to know some Buddha's teachings, we need to meditate and finally, we need to apply the results of the practice into our daily life. What is the point of meditating for hours if straight after the session we harm our friends by our inconsiderate behaviour?

It is always good to ask or remind ourselves why we meditate. If we want peace of mind, we keep checking whether we are able to remain calm in stressful situations. If we want to get rid of our ego - we check how we react when people offend or criticize us.

Personally, I never did a regular breathing practice on its own. I met Mahayana/Vajrayana masters and got attracted to the possibility of realising our Buddha Nature by applying certain methods. So I use those methods to realise my full potential in order to help other beings (Bodhisattva vow). In everyday life I keep checking (among others) whether I remain stable and joyful in difficult situations and whether I can feel compassion to all the beings no matter what they do. 

Some may say that the next stage after Breathing meditation is insight meditation (Vipassana). However, before starting a new practice, you should very honestly check your motivation and goals - what exactly do you want to realise? Also make sure the new practice can indeed bring you closer to your goals. In general, keep checking whether your current meditation practice brings some positive changes into your everyday life and if you feel that there is something more you want to realise - try to find a new practice that will help you achieve that.