Experience will be your guide on this on. Been doing rewires for couple of years now. Was terrible at estimating first few go rounds. Now I can hit numbers within a couple hundred and hours within 4 on a 1800 sq ft rewire
I think this is the best thing to keep in mind. It sounds like you are a solo act. If so, let's be frank, if you miss on your the first bid you get, it is just your time that you lose. (not talking stupid low here) That said, definitely don't use a square foot method. If you want to get in to this and stay in it, take the time. Think about every aspect of rewiring a component that can be repeated, getting the tools and material to the location, cutting rock, removing insulation, securing the power, demolishing the wire, running new, cleaning up, hauling debris off, patching walls and holes, and on and on. Assign a labor to it, and get actual material prices. Do this for say, one receptacle or one switch, and then multiply by the number of locations. Do this for each unique item especially at first, as in, GFI, switch, 3 way switch, duplex, light outlet. After you do this a couple times, then start taking short cuts, like counting all outlets and just adding $10 per GFI, etc. If you do this, you will miss your mark on some things, but the law of averages will balance the pluses with the minuses as long as you don't think too much and you trust your instinct and experience.
And, as other advice, if you don't get the job, try to find out who did and what for. Go back see if you can get to that number. If not, don't worry about it, try the next one.