I too just started Remicade, but haven't received a bill from the infusion center yet, just a $45 bill for the medication itself. Two things:
1) Before I received my first infusion, I sent in all the paperwork for the RemiStart program, and was approved. They told me that as soon as I get the EOB from my insurance company I need to mail it to them and they will mail me back a debit card for the out of pocket amount, and I just pay my hospital bill with that. Luckily I have a $1500 out of pocket max and then the insurance pays 100% once that's met, so if RemiStart allows $3000 (which would be technically me paying out of pocket in the hospital's eyes) then I may never have to pay any bills except for the medication copay. You should look into it more and see if this may be the case for you.
2) Where do you get your infusion done? When I set my appointment up, they told me that if the hospital ordered the medication it would cost me $800 per infusion. BUT if I called the prescription insurance company myself and ordered it (my doctor just had to fax over a script) and have them mail it to the infusion center, I would only have to pay a $45 copay, so this is what I did. Perhaps something like this might be an option for you- I was lucky in that the lady I dealt with at the infusion center was very helpful and concerned about saving me money; unfortunately a lot of hospital employees/doctors offices are not like that.
Good luck and I hope you are able to get things sorted out.