Water go slow in bathtub, and bubbles in the toilet

Wonder if you have a Drain or Vent Problem?
Maybe try dumping water down the Vent on the roof.

I wouldn't climb up on the roof just yet. This isn't a vent blockage. You have a partial blockage downstream from the tub. Here's what to do.
Unscrew and remove the overflow plate,(The one with the drain lever) and pull out the tub stopper. You now have a clear shot at the trap. The way you were going in through the drain it ran you square into a tee that you can't get around. Now feed the cable( 1/4" best or 3/3" with a small tip. You can rent a Ridgid K50 sink cable.) About 2' down you will run into the bend of the trap. Crank and push at the same time to work around it. Your blockage will be found in the lateral pipe going to the stack. You shouldn't have to put out more then 10 or 12 feet. I have found tub and shower clogs to be mostly hair and the worm should auger into it and pull it back. After you snake pour a few pans of boiling water down the drain. This will loosen the grease and flush the mess out into the main. Hope this helps and thank you for rating my reply. TOM

I would trust Speedballs advice.

Im with Tom on this. You need to snake a drain. I, however would go about it from a different approach. I would pull the toilet and snake from there with a large auger and bit. The fact that your toilet is bubbling when the tub drains means your partial blockage is in at least a three inch pipe. To clear a three inch pipe correctly you need a snake and bit big enough to do the job. Running a small snake and bit down through the tub may clear the clog temporarily, but most likely it will back up again in short order. Just my thoughts on things. I think we would all agree that you wouldn't snake your main sewer through an 1 1/2 cleanout, correct?