Make It, Build It, Dream It. Creativity.

Since you don't have clamps, is there any way you can use cord/rope to tightly secure the legs against the seat as it's drying? As long as the legs fit into the joint tightly, I don't think you should have too much of a problem using cord. It's not THE best solution, but it's good for a quick DIY fix. If the finish bubble doesn't bother you when it's covered, I'd say don't worry about it and pretend it's not there. On the other hand, if you want to have a go at refinishing, there's no real reason NOT to.