Bespin is primarily floating cities and gas clouds. There are multiple cities there, but only Cloud City has any particular development. We have wiggle room, but any politics should probably take place in the area that actually has backstory and environment. Plus, I don't believe our delicate ambassadors really want to deal with an entire cavalcade of Ugnaughts.
A couple of suggestions, for each possible sphere of interest.
Military
- The local Ugnaughts, opposed to rule from a humanocentric, Fascist power, stage an uprising in Ugnorgrad. This gives them home field advantage and makes them a challenge to take down. Plus, "the Massacre of Ugnorgrad" looks really cool on our resume.
- Since there's not a lot of physical ground on Bespin, the infantry detachment we sent was intended to be more of a show of force, rather than a conquering army. During a dress parade to properly intimidate the locals into submission, they weren't terribly intimidated. Suddenly bombs. Suddenly crossfire. A resistance force catches us by surprise, and we have to whip up an immediate and decisive counterattack.
Political
- Contract negotiations seem like the obvious direction to go. Bespin is the single largest tibanna manufacturer in the galaxy. They sell to a lot of people. Taking over the planet might very well be as simple as buying off their contracts...while generously undercutting their asking price, of course.
- I think it would be hilarious to see our diplomats attempt to negotiate with Ugnaughts. They're short, ugly, smelly, blue-collar workers who are heavily resistant to change and prone to paranoia mildly excessive caution. They are, however, the primary workforce of Bespin. If they cave, the planet has to go with them.
Espionage
- No one gives up their most valuable secrets willingly. Once your employers know how to do your job, they can replace you. As such, the Bespin authorities have decided not to explain their more advanced gas processing techniques to ensure they have an ace up their sleeve. It'd be a shame if we were to inexplicably find out anyway, robbing them of that advantage.
- Bespin does a ton of very legal business with everyone in the galaxy, but there isn't a corporation that has ever existed ever that hasn't bent the rules to make a bit more money. Uncovering an illicit deal with a high-profile client would give us major blackmail potential to either ensure their immediate compliance or their future loyalty.
Naval
- Man, it sure would suck if all of the satellites orbiting Bespin, and thus allowing them to contact the rest of the galaxy for trade agreements and/or assistance with resisting a military occupation. It'd be a shame if we happened to them.
- Establishing a blockade is easy. Holding one is significantly more interesting. The First Order blockade is being faced with a boatload of smugglers. Zerg rush tactics means that it's impossible to keep them all from getting through. Unless, of course, you're a PC.
