This is Luke on Bespin. You can tell from his clothes. The "Bespin fatigues" as they are called on the action figure box even though its the same outfit he wore on Dagobah.If you will recall, Luke flies to Bespin from Dagobah in his trusty old X-Wing fighter. And when he is flying it he is wearing his trusty old X-Wing fighter outfit, which is orange.
After he lands on Bespin the first we see of him he isn't wearing his orange X-Wing fighter outfit. He is in the above Bespin fatigues.
If there is one thing that I think all reasonable people can agree on it is the fact that the X-Wing fighter is way too small to have a changing room in it. And I think it is safe to assume that he wouldn't have gotten changed right there on the landing platform with everyone watching.
That means that right after landing, he had to get out his travel case and look for the nearest bathroom to get changed in.
I wonder what the exact sequence of events was between him leaving his X-Wing and actually getting changed. I imagine that the bathrooms nearest the landing platform for an X-Wing would probably be similar to those in a gas station - dirty and not very private.
Did Luke balk at using those? Did he walk in, take one whiff and promptly walk right back out? Or perhaps he found that the stall door didn't close properly and simply didn't feel comfortable with the whole set up?
If he did, his next logical step would have been to try and find a bathroom in a more upscale part of Cloud City. In a big complex like that they probably have maps posted on the walls here and there like they do in shopping malls, so he would have needed to seek one of those out.
On finding the map, he'd probably discover a few options. Maintenance? No, the Ugnaughts probably use pretty small facilities. The restaurant area? Well, they'd probably have bathrooms, but you might have to wait in line. Residential? Probably no public bathrooms there as everyone has their own in their apartment. The retail district? Bingo!
So he'd be off to the retail section of Bespin in search of a good bathroom to change in. Still in his flight suit he'd probably draw a few stares, but whatever. They'd be a small price to pay for avoiding the indignity of getting changed in that awful landing platform bathroom. He'd probably also need to pick up a few things at the shops, so using the bathrooms in the retail section would allow him to kill two birds with one stone.
Then, after changing and freshening up, he'd probably head up to the carbonite freezing/ prisoner detention level to get on with business. As we don't see him carrying any shopping bags when Boba Fett takes a shot at him, he might have stopped at a coin locker or even gone back to his X Wing (having just arrived he probably didn't have any Bespin coins) to put away his purchases on the way.
And from there the movie regains the narrative.
