You should definitely tell school A about school B's offer. I would send an email to your potential grad advisor and cc the grad coordinator for your program. This will let them know you are a desirable candidate and they better hustle. I recently did this and got better offers from both schools I am seriously considering; unfortunately, this has made my decision much more difficult. You should also visit (if you haven't already) and ask if they provide reimbursement for travel expenses. Graduate students bring prestige to a university, they want to attract the best and they can usually make things happen ($) when they want you. Also, if you really truly want to attend school A, just remember that a lot of what you will be doing aside from loads of homework is applying for funding--its a never ending quest for cash so you can do what you do. Might as well go to the school that suits you best and make sure you get your hands on some funds, after all, its practically your job in grad school.
Best of luck with your decision!