Am I responsible for my mothers bill at the assisted living center because I'm POA?

Yes I wish they would have told me that.

Twright, make sure from now one when you sign something for your Mom, you do what cwillie above recommends for the signature.

I remember when my Mom needed to live in long-term-care, there was a ton of paperwork I needed to sign as POA.... the Admin told me to make sure I signed as POA for __________.   I was glad the Admin told me because I was so overwhelmed that I couldn't think straight.

Hope everything works out in your favor.

She is renting her house and we had to evict the tenants and she needed that income to stay. We are paying the bill in instaments now but I told them after I got her home and I know what her cost would be for the home care she needed that I would get back to them and let them know what she can afford each month to pay the balance she left (she was behind one month). They did t like that they reported me to social service that I was spending my moms money a week after she left. Thank god I save receipts for everything!. They investigated saw I wasn't spending my moms money and closed the case. I think that pissed them off and within the week the filed a judgment against us.
Yes I just signed my name I didn't know and they never told me by signing I would be responsible for her bill.
I only sign POA on her checks when I pay her bills.

It depends, when you signed did you remember to sign as Twright, POA for Twright's Mom? If not you may be in trouble.
Even though your mom had to leave she still owes for the time she was there, why has SHE not paid? Did you not understand the costs involved when she moved in?