I have earned the Tumbleweed badge for a question I posed as week ago... and I'd rather have an answer than a badge. :)
Is offering a bounty the only courteous way to "bump" a question? I'm fairly new and would like to behave appropriately.
I'm assuming you are referring to this question?
If so, there is noting wrong with the question and no great reason why it hasn't got an answer - I've performed a minor edit to remove the unnecessary 'thanks' which will bump it (I wouldn't normally edit a post just to do that) - but as you say the way to draw attention is to offer a bounty.
Bumps without bounties are appropriate if the question is modified in a way that makes it more clear or brings new information to light. Normally when you ask a question you are also doing research on it yourself and perhaps even trying some things that provide partial answers to the problem. Posting this information not only provides a bump for the question, but also may make it clear to someone what part of the solution needs to be understood. You are welcome to do this as often as you can improve the question.