I've got a 2001 Bonneville SE, am I correct that it has a 4t65e transmission? Also do the shift kits for these generally take care of the pressure control solenoid problems, or does the solenoid have to be replaced?

Yes, I believe you have a 4t65e. No, installing a shift kit wont fix a PCS problem. And I don't suggest installing a kit unless you have all the transmission problems fixed.