I will comment that I'm not really easily embarassed now, but it didn't seem that embarassing.
The waiting room was probably the worst at the beginning. You know everyone has a pretty good idea why you are there, but then I rapidly realized that I didn't think poorly of anyone else there, so why would they? It was early and I hadn't exactly slept well the night before so I was tired as well. Also worried they'd find a bunch of crap in me still*
Changing was in a curtained nook, though the nurse did specify to take everything off including underpants. I guess maybe some people don't. I had a cloth gown which could be wrapped around me. They put an IV just in case, I met the doctor, then got a mobile bed ride to the endo suite through a surprisingly long maze of corridors.
Three people plus me in the suite. Doc goes over basics, then roll on side in Sims, bend legs. Butt exposed but genitals mostly covered. Spread buttocks for quick lube and about ~1 sec DRE to check for how the anal canal goes, then a quick insertion of the scope and after that no one was looking at my butt, it was all on the screen. Going in I was a bit worried of whether the pressure on the prostate would cause an erection, but there wasn't much and even if there had been it would have been hidden by my legs (and no one was looking there anyway). I looked for a very experienced doc, things went quickly and there were some parts that felt odd and a twinge of discomfort but no pain (he used liquid inflation to advance the scope, which causes less cramping. Also the most expensive "enema" of my life - though they used the suction to clean out the liquid as the scope went up. TBH that was something I was a bit worried about - would I spray the water everywhere. But I didn't.
Was thinking I could tell everyone I had done the colonoscopy and things were good and I wasn't going back but then the doc found polyps... neat to see how they did everything, but now I do get to go back much more frequently. On the plus side the doc is good and they do have a drug-free option so I am actually OK with it, beats CRC (seen that a couple times). Was sort of planning that this one would be clean and I'd do a barium enema for the next. Ah well - that would probably be more embarassing really. Note that I'm not saying you gotta do it drug free, I just don't tolerate drugs well and also would rather know what's going on, so this worked for me and drugs would not have.
*yeah, the prep is not fun. I'm slow and unpredictable bowels so the simple things were out. I had to not eat berries and many fruits for 2 weeks in the height of summer... not gonna make that mistake again. Then a two day prep with mag citrate and the 4L jug of awful liquid that almost made me vomit - and it was still mucky at 4:00 in the morning, so I rushed out the enema bag and frantically took 3. It got to "OK prep" but next time I will leave myself more time and plan on the enemas.
Having (a) seen the studies showing the need and (b) had them find polyps before 50 I'm now in the "go and do it. Just do it... it can prevent cancer."
That and check your skin regularly.