Help with bathroom leak

Hi there,
I'm new to this forum and hope someone can help me. I am a single mom who just purchased her first home 3 years ago. It's a 92 year old tiny house and I love it. Well, after moving in found out that the basement leaked, the roof leaked and now the bathroom is leaking! Had the roof fixed this summer and had the basement waterproofed and foundation repaired......but that's for another forum.
Anyhow, suffice it to say that while I feel the kids and I should probably wear lifejackets to bed, I am hoping to find solutions to my rainy day problems.
I started to notice an occaisional dripping sound downstairs when someone would use the bath or shower. Of course denial is a wonderful thing!
Then, last year another problem started. When someone would take a shower, water would run into the ceiling below. The bathtub is right over the stairs and you could actually see it flowing down the wall! So, I put a stop to showers. This summer I ripped up the tiles from the base of the tub by the taps up to the shower head. uh huh, no leak there. I know there is still leaking into the ceiling as it is getting worse. Now I'm not sure if it's coming from the bath or the vanity sink.
My question? I have replaced an entire bathroom before, so think I can do this.....but am very tight on funds. As I only have one bathroom, I'm trying to decide the best method of attacking my trouble.
Should I tear up the ceiling below the bathroom (in my living room and stairwell) first, to determine where the leak is?
Should I rip out the tub first? and then repair the ceiling if needed?
To access the end of the tub, I would have to take out the upper wall halfway down the stairs. I'm just not sure where to start and don't want to have to call in a plumber unless I find it's something I can't deal with.
Suggestions anyone? I really look forward to your advice.
Thank you!
Klamity

Don't cut any ceiling out. I would bet it's fixable by working from inside the bathroom.. A house that old must have an access door or opening so you can really see the backside and under the bath tub.

A plumber could make a living repairing your kind of leaks and most times it's not a plumbing leak. It's a caulking problem and/or the person taking a shower is getting water on the floor and that is getting through the floor and onto the ceiling below.

Remember, you cannot water proof the bathroom floor.
So tell everyone to shower and keep the water "in" the tub.
Once had a customer had a wet ceiling but it only got wet when one of her kids took a shower. She finally talked turkey to him and he finally got the message. And this was in an upscale home.

Thanks so much for your quick reply. The only access to the area behind the taps and shower pipe is through the wall above the stairs. I live in a story and a half and the stairwell runs directly under where the tub is. Sorry, it's hard to describe. I could open the wall near the bottom of the stairs that would open up into that area, but it would still mean drywall work. I'd be much happier doing that, though.
The ceiling below the bathroom is showing obvious leak damage. It's a popcorn ceiling and the seams between the drywall are cracked and showing. Where it seems to be settling is directly under the vanity sink. This is what has me puzzled, because I KNOW that when showers were taken (before the 'ban') it would leak onto the ceiling. But there have been no showers allowed for months now and the damage is getting worse.
It's either the tub area and as water follows the path of least resistance and gravity, it may end up directly under the vanity but I just don't know.
I just don't want to rip up the whole house if it is not necessary. I could start with the wall behind the taps....just a small section. If I want to replace the tub, can I do this without going through the ceiling below?
Thanks again,
Klamity

I would measure and cut an access then in that stair well and make it a permanent access. Remove the spout and take the handles and escutcheons away from the wall and caulk that area and reinstall those items.

If you could look at the backside with a good light and then follow the tell tale signs of water, it well speak volumes.

You could even have one of the kids take a shower and look for dripping......

Thanks, Plumber1.
I'd have them take a shower but since I have removed the tiles at the faucet and shower end.....I'm pretty sure it would leak! haha
I will try as you say, though, and open up that one end and see what I can.
I'll keep you posted!
Klamity