OTOH, if you want to do fixed bids, you better have a really good idea of exactly how much time it's going to take you. This means that you should concentrate on doing only things you've already done, or that are very similar to them. Otherwise you'll run into something you didn't even know you didn't know and blow your estimate and eat the losses yourself.
I've raised my rates at least a dozen times over the past decade, and not a single client has complained. It just requires clear communication and a reasonable ~month's warning.
Also, who says you are stuck at your initial rate? Whenever you want, you can increase it. Many clients will have no problems with this, if you are worth it. Some will, but that's typically the kind of clients you can afford to loose anyway.
Secondly, tptacek is right again. Once you bid $125/hour, you're stuck at $125/hr. Even if you save your client that $2,000 month for 5 hours work, they`ll expect to pay you $625 and nothing more.
Be warned, this post is spot on if you always want to earn the same amount of money but you will never grow a company with this billing method.