Bathroom tub leaking

It's possible the water is getting around your shower, possibly where the tile meets the tub or pan (if you have one), or behind the fixtures, or even around the door (if any).

I would check all of these and recaulk where appropriate before going in for wholesale destruction. Try splashing water by hand/bucket on areas you might suspect and see if that leads to leaks.

Or maybe you even have leaky plumbing in the wall. Do you have access to see in there?

There is a clog downstream from both of these drains. If they are both at the lowest level of the house and you have a septic system, then it's conceivable that the problem is there, but you'd also see water backing up into that bathroom when you run any other showers/toilets in the house.

Most likely, the clog is in the joint in the drain lines where the shower and toilet join on their way out of the bathroom. Get a snake to fish down the drain (probably best to do this in the shower to avoid damaging the toilet bowl) and expect to go down quite a few feet before you reach the problem.

Edit: Revisiting this question, I'd agree that there's also a likely vent blockage from the bubbling descriptions. But the fact that toilet water backs up into the shower points to a drain blockage, too, and that will be easier to fix.