Every now and again I see a question that I would like to know the answer to but don't know how to solve. I don't mind offering bounties but since I don't have a ton of rep, I'm wondering if a bounty of 50 or 100 is seen as 'rude' to put up on someone else's question.
It is fine to place a small bounty on someone else's question. The principal way* that doing so affects the author is that they might suddenly get a bunch of notifications about their question, which is typically welcome (although potentially surprising for old questions). If you're unsure of any particular case, you can use comments to ask the author about offering a bounty. The size of bounties is largely irrelevant - they all work about the same for drawing attention and are unambiguously a form of positive feedback for questions/answers.
*This answer would be incomplete without mentioning that placing a bounty prevents any other user from placing a bounty until yours expires - but this is a really minor problem; it's rare that two people would wish to bounty a question at the same time and not much harm occurs even if such a conflict occurs.