Personally, I would do more mark-up on your labor and equipment. They don't need to know how much you're charging, but you need to make a decent living, pay your taxes, pay the fuel, light bill, wear and tear, all the time you have into bidding etc....
If it's not a job anyone is likely to bid on, or others are bound to bid high, just because your current overhead is low doesn't mean you have to work cheap. $40 per hour sound cheap until you figure in all the incidentals before and after and all the oh $h!t breakdowns that pop up.
I know where your coming from, I started the same way, but just last night the wife and I had a knock down drag out (not quite) over my rates. She insists that $100 per hour is too cheap and we need to make more to cover bills. I say I'm still the highest around so it's good enough. My phone is ringing off the hook, so I must be doing something right.
You'll do ok on this, keep a file with notes so you can refer back when you get something similar down the road. Good notes and receipts can save you later when you are scratching your head on the next one.
Good luck!