now the tube bulges out of the tire
It's likely time to get another new tire - this one is probably dead.
The tube bulging out of the tire means that the structural integrity of your tire is compromised - one of the functions a tire must do for you to ride safely is hold the tube securely. This tire no longer does that.
And a patch really can't fix it. The fibers embedded in the rubber compound are likely cut. It's those fibers that give the tire the strength it needs to hold the tube in place against the pressure of the air inside the tube, and no patch can uncut those fibers. A glued-on patch can fail, as the glue is not really designed to take the shearing forces that are pulling the tire apart at the cut. The tire's fibers are designed to withstand those forces, but they're cut.
If you do the math, the total forces put on the rim and tire by the air inside the tube are pretty substantial. For example, a 1.5" 29er tire has an area over 410 square inches (area of a torus). If that tire is inflated to mere 50 psi, that's a total of over 20,000 lb of force spread out over the area of the tire trying to pull it apart and push it off the rim.
A tire boot (as mentioned in what's currently the other answer) is, IMO, a temporary fix for a cut tire. It gets you home.
Tires are wear items - they wear out, sometimes faster than you'd like.