Question: I'm an undergraduate student that was offered a role researching for a grant. I was able to get authorship status on a paper and will be attending a conference for it later this year. The professor I am working for connected me with another student at a different university in order to share a hotel room. We will both be staying for the entire week and are responsible for booking our own reservations. Unfortunately, the centre the conference is located at is booked, with only a single-bed room available that we would be required to vacate on Wednesday then move back in.

This student was fine with booking the room and asked me if I was okay with it, but after I realized that it is a very small, dorm-like room with a small bed and no futon I counter-offered a reasonably-priced room at another hotel a half-mile away with two beds that we would not need to move out of midweek. I thought this would be well-received, however the student pushed back saying that the other room had a better price (of course, as it was intended for one person or a couple) and we would have better involvement with the conference (doubtful, as long as we show up on time).

Besides already being an incredibly poor sleeper, I'm otherwise just uncomfortable sharing a small bed with another student I don't know, and the room is small enough that I can't confidently say a hotel cot would fit. However, I also don't feel comfortable making this a bigger conflict than necessary, and I don't want to upset my professor by costing our grant more money than necessary by booking my own room at twice the cost. On the other hand, I do feel I have the right to request sleeping accommodations that I am comfortable with. How can I handle this appropriately without offending anyone?

Answer: 
You may just need to come to the conclusion that no negotiation is possible and make your own arrangements. No one should be offended by someone who wants to preserve their personal space and privacy. 

I doubt that your professor, who is the only one, other than yourself who matters much here, would think less of you if you don't yield to a situation you find somewhere between uncomfortable and untenable. 

There is the financial issue of course, but your privacy is likely worth the cost and you will have a much better experience at the conference if you are comfortable personally. While cost isn't a factor for me anymore I often tell family (cousins, kids, etc) I'd rather get a hotel than use their guest room. Privacy, comfort, personal space. 

That said, you might take a bit of time at the conference to see if the other student is someone you might want to be friends and colleagues with generally, but that is a question for the future. 

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Due to a comment, perhaps I should be more clear and explicit. This is not something you should accept if you have any reservations. You are perfectly correct to reject it.
I do not know this person, but I would simply say it honestly. It's perfectly professional. Say something like "I understand that the room is a bit more expensive, but I would much rather find a room that accommodates two people and does not force us to share a bed. This room is the best I could find, but if you can find a similar one for a better price, send me a link."

This is a perfectly normal and reasonable thing to want, it places no obligation on you to pay a greater share, and it should not offend any person who is there in a professional capacity.