The bearing should be held in place by nothing but the c clip. If you have that off it should come out with the top collar, then pop it out from the backside of the collar. There's a rubber sleeve around the outside of it, and, believe it or not, a metal staple (?!?) in the rubber that helps to hold it in place in the collar.
Some advise about your swap. I usually pull the whole column out of the car when doing the swap, because you may want to remove the shift tube. It 'might' get in the way of the bottom collar. I've never tried doing a swap where I left the shift tube in place, so I can't say. Try it, and let me know.
I usually have to paint the collars, so I usually bead blast all the other parts and paint them while I'm at it. Once the collars are off all that's left is the collapsible tube and the center shaft. I rebuild the steering coupler pot coupling then, too. Usually the rubber seal is wasted and the grease has turned to tar. It can be a PITA to get the steel clamp back on the pot coupling but it's doable with a vise to crimp the metal tabs around the raised bumps in the end of the coupler.
If your bottom collar uses a return spring for returning the collar to its normal position after unlocking the key, you may need to drill a small hole in your collapsible tube at about the 11 o'clock position. One more reason why you may want to pull the column. See this picture - hope this helps.
