~A bit late , but I figured I'd share my experience as well, for the sake the next guy wondering and also, googlers. :p
After my hysto this spring and my recent top surgery, I woke with a catheter. While it was never mentioned on beforehand (on? in? suddenly, language derp), I had assumed it would be there, so there was no surprise. For me, the worst part would have been the insertion, and as that was done after I was out, the catheter never bothered me. Also, it was a relief to be able to wake up and not have to deal with a bedpan (been there, hated that, hope never to experience it again!) or having to get out of bed before feeling ready.
After the hysto, it was removed while i was in the recovery area, shortly after I was awake enough to sip some tea, have a small bite of food, and assure the nurse that I felt able to stand on my feet for a moment (I didn't put it to the test until after it was out - phew, I was right XD )
After the top surgery it stayed in a little longer, until after I had been in my own room for a while. I think I took a bit longer than usual to wake up, and was drowsy for quite a while after that. I honestly can't remember if I had a go at standing on my own before they removed it this time, or if they took it out first.. In any case, I don't think I had it in for more than an hour after returning to my room.
While the removal felt awkward and very uncomfortable it was over quickly and soon forgotten. I was glad I didn't have to keep it for long, because I always feel like I "have to go" a little when I have a catheter in. I had one for quite a bit longer after a surgery 20 years ago, and because of that feeling I was always worried my bag was full and that it would have messy consequences. >.>
(Since experiences vary, I think I should add that I don't have all that much bottom dysphoria, and naturally this will play a part in how people experience this. For instance, I didn't have much issue with gyno exams (for comparison, I can't decide which is worse, that or the dentist.. well the dentist hurts more, I guess). The awkwardness of the situation up until I'm alone with the doc is a lot more stressful for me than the exam itself.)