If all the bills are in my name, and the roommate is moving out, what steps can I take to ensure payment of final bills? Legally can I do anything? Sue them if they don't pay?

You should do your best to get them to sign a statement, showing the amount of the bills that remains unpaid.

State the terms, how long they have to pay it, if there are set amounts over a weekly or bi-weekly period, spell it all out.

Then, if they do not pay as promised, yes, you can take them to small claims court.

Without anything in writing, it will be your word against theirs, and who the judge chooses to believe.