Plumbing – Why is the toilet bubbling

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.

This sounds like your leach field is possibly blocked. That's the disaster scenario where you not only need the tank pumped, but the yard dug up and a new field placed.

Water from your laundry coming up in your tub is a sign that it's not draining to the septic system. This is either because there is a block in the system before the tank or because the tank is unable to accept any more water as it is plugged on the discharge / leach field side.

When I opened up the clean out pipe clear water came out (about ten gallons). I shoved the hose down about 25 feet and it was running full force but it seemed like all the water coming out of the hose was draining back out of the clean out pipe.

... and that's the sign that it's doing option #2: the tank is full and failing to drain.