Don't discount the amount of work you may be able to do yourself, even in a state which requires licensed plumbers for inspections. You may be able to:
Demolish whatever's currently in the space that will become the new bathroom
Frame the new walls
Do some or all of the rough in plumbing work
Install fixtures after a plumber has completed the rough-in
Tile, paint, trim
I am finishing a total re-do of the plumbing and bathroom on a house we bought in January. I have a background in carpentry, I'm handy and have quite a few tools, but I had never done any real plumbing before.
The job included gutting the bathroom, repairing joists, floors and walls, and tearing out all of the old plumbing (cast iron drain pipes, hodgepodge of galvanized, copper, and PVC supply lines).
We then put in all new PVC drains and CPVC supply lines, reframed the bathroom walls and floors. We installed a new tub and custom tile around the tub, walls, and floors. I got the tile from our local ReStore (Habitat for Humanity store) for $50! The toilet went in yesterday, and I hope to have the final item (a pedestal sink) in tomorrow.
Our total renovation cost so far is at $4176, according to my records in Mint. This includes $350 in labor paid to a friend who helped me do the tile, a few tool purchases, fixtures, some framing supplies for areas other than the bathroom (garage side door, floor joists).
Just thought our similar job might give you some food for thought!
Edit: I screwed up on the Mint cost calculation, and just fixed the number above. This cost includes everything from paying for an initial inspection, paying an electrician so the city would turn the power on, supplies, etc. etc. Since I've been working on a rather leisurely schedule on weekends when we're not traveling, I've been able to absorb most of the cost in our monthly budget.