Well, I would put the 40 K up there for a couple of reasons...ballparkin wise of course.
First is you will need a drawing and permits, by a professional it will cost 1k right away.
Next is cleanup,tarping, plastic inside, dumpsters, man hours vacuuming and hauling material, covering material, prep work for the entire job as it goes...5K
Then comes the actual demo work and getting the project ready for new framing, 2K
New framing and modifications...5k
Plumber, and fixtures. 5k
Siding, paint and roof repairs 4k
Heat to room 1k
Tile , walls? floor 1k
Everything you don't see, have to figure out as you go and have not figured into the addition as you go...5k
Now add some profit for the GC and the other unseen upgrades you want...jacuzzi tub, claw foot, stand up tile shower in terrazzo marble...only you make up that budget.
OK so I'm around 30k....however....
You can easily project 40k for a good ,enjoyable bath.
I always tell someone to get a couple of prices, and budget 30 percent more always for unseen issues. Keepin the wife happy is one. Then going out more often to get away from the job is another. And don't forget all the coffee and donuts for the crew once and a while...you need to keep them happy to get a good job.
Time of year may not matter.
Ps...having not even looking at updates to mechanical and service...that's why it is a ballpark. You may even have to run new supply to the bath if you only have half inch lines. Getting water to another bath on the 3rd floor you may need new 3/4 lines just for good volume and pressure to the bath. Plus upgrades to the home, now you will have to bring the house up to current standards and codes where they want you to improve. Talk to your local building official for any new updates which are mandatory. I know you will need to update the smoke and carbon monoxide detectors in your area...adds more money. Good luck.
Living in the MA, CT area...those are the ballbarks.