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It's probably just semantics but to me, that's not a "fixed price bid". It's time and materials mascarading as fixed price.
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Well, I think it's a Third Way (he said, with his best Bill Clinton smirk). I guess what the advice that I would offer Michael is this: many clients want to avoid time/material bids, but they might be open to a range -- in other words, "I anticipate that this will take from 10-15 hours of my time. What I would like to do is charge an hourly rate, with a guarantee that the price will fall within that range." In particular, I have found smaller clients very open to this approach. That might (or might not) be the case here.