Sounds like your turtle needs more hand-feeding & attention. That has broken the biting habit in my turts in the past.
Most RES/painted turts don't bite unless they feel threatened. RES's in particular are not known to be very aggressive (compared with snapper or soft-shell turts which are very aggressive!). They flatly do not want to open their mouths unless food is involved. Soooooo....get food more involved. Always feed a little bit by hand at every feeding so they get used to associating your hand with food. A way to a turtle's heart is thru his/her stomach. One thing I used to do with one of my RES's many years ago was to take his daily feeding, divide it into about 5-6 pieces, then every time I go by his tank, feed him one of the pieces. You are still feeding the same amount, just dividing it up so you do a lot of "repetition" with the turtle. They see you, and WHAM there is food there. Turtles have a very small brain, but they can learn where their food comes from.
Also, put the tank in a very public place where a lot of people walk by. This gets them used to seeing people all the time. Talk to the turtle a bit when you get a chance too so they get used to human voices. They will be used to all the traffic after a while and realize that it's no big deal if you are around (and once in a while give them a pellet of food).
Be very patient with this process. Just shower them with attention. I promise you will see results after a while.