Sounds like the main drain for the bathroom may be restricted.
As you shower the water doesn't drain away fast enough, and the plumbing begins to fill with water. As the pipes fill, air may be forced out through the toilet trap causing "bubbles". Since the tub is the lowest drain, the water backs up there first. If you continued to shower, you'd eventually see the toilet overflow as well (if the tub edge is higher than the toilet rim). If the tub was deep enough, you'd eventually see the sink overflow too.
If you look at this crude representation of your bathroom, you'll be able to see what I mean.
Now, if we add in a clog we can start to see what happens when you shower.
As you shower the water cannot pass through the clog fast enough, and the pipes begin to fill.
At this point, any air trapped in the line between the drain and the toilet trap will be forced out and bubble up trough the trap.
As you continue to shower, the tub is the first to back up.
Eventually, if you shower long enough the toilet could also overflow.
Depending on the height of the sink, quite a bit of the bathroom would have to fill before it overflowed.
The first thing I'd try is to clear the drain using a Plumber's snake. A hand auger would likely work, and can be purchased at a local hardware store fairly cheaply. Drill powered augers are also available for a bit higher price, but require a bit more of a gentle touch (and obviously a drill).
Another option is that the vent for the bathroom is clogged, or not sized appropriately. If vent stacks are not covered properly, leaves and other debris can become lodged in the pipe and prevent air flow. A clogged vent will cause the fixtures it's venting to drain slowly, and the results can be similar to a clog as described above.
As with the clog, the solution to clear the blocked vent is a Plumber's snake.
Foul odors are usually due to the water seal in the P-trap failing for some reason. Sometimes the water simply evaporates in little used fixtures. Probably not the case here. The other cause for failure is the lack of proper venting. Without a proper vent, the water seal gets siphoned out of the P-trap after the fixture is used.
If you have an air admittance valve serving as a vent, it could be failing to open properly, or it could be stuck open, allowing sewer gases to enter the room via that path rather than the P-trap. These devices should be accessible. Simply manipulating the valve disc by hand can dislodge it from it's stuck position and allow it to work again. Or the device might have failed and needs replacement.
You quite possibly do not have an AAV, but the more common vent through the roof. This time of year in Northern climes, the vent could become obstructed by ice or snow. Simply clearing the blockage will solve the problem. It's also possible a bird decided the vent would make a nice warm nesting site. Other vent problems could be more endemic of the installation itself, being either undersized or even non-existent or otherwise ineffective, or an alternative, less effective, trap arrangement such as S-traps or drum traps. If you've lived there for a while and the odors just started happening, these endemic issues are probably unlikely.
Best Answer
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.