I don't like może mógłbym (two words from the same verb móc in close proximity generally sounds worse in Polish in my non-native opinion).
"Może" is a particle, inot a form of the verb "móc". It means, in this context, "perhaps".
The phrase "może mógłbym" is perfectly fine and commonly used in Polish.
Może mógłbym Ci kiedyś postawić drinka? - sounds v.polite. By using this version you're politely asking for permission to buy somebody a drink.
Postawię Ci drinka kiedyś, dobra? - implies familiarity and is kind of rough, especially the "dobra?" question tag. Said to a person you don't know very well it might be even perceived as borderline rude. IMHO this version does not give the other party space to respods; their agreement is sort of implied and imposed upon them. I wouldn't use this version to woo someone.