1. Dont put the bank details on the PC to start with.
2. Did you mis-use the details you found? I guess not. The same will probably be tru for those who find your details.
3. a single over write with new data will compleatly remove the old data from the disk. If it did not, how would the disk know how to tell the old data from the new stuff?
So, find the file that contains the data you want to protect, open it, delete it's contents, and hold down a key till you get bored. click save. this will over right the file with the new version (all xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx) get the picrure). so now old version gone.
Then to be more paranoid, delete the file, and optimise the disk.
But if the stuff is so sensitve, take the hard drive out before selling the PC, and put it in a bonfire. If it's that inportant, YOur boss in MI5 will give you a new PC anyway.