What you will need to do is sound insulate all the walls of your bedroom that attach to the interior of the home. You can ignore exterior walls.
First remove the sheetrock and insert solid core insulation. Some of the solid core has noise attenuation numbers on it. Home Depot carries it, and you can check with them on which is best for your area. Make sure the solid core fits securely in the opening, no gaps! I have used the paperback pink insulation, and it works quite well. A couple of contractors have told me the solid core is much better.
Another option, which is more money, is spraying expanding foam into the wall. If you do this, you won't need to pull out the sheetrock. But you will need to put another layer of sheetrock over the top of it with an air gap. Use 5/8 inch Sheetrock for this. Maker sure this second layer of sheetrock doesn't secure to the wall. Secure it only to the edges of the wall, so the gap is open and not touching the wall itself.
If you went with the first approach, you will need to replace the 1/2 inch sheet rock with 5/8 inch. Then put your second layer of 5/8 inch sheetrock over it with an air gap as I mentioned..
The door needs to be treated. Since this is a bedroom door, it most likely is a hollow core door. You can drill holes in it and inject expanding foam into it, although the holes will be hard to conceal. Another option is tacking thick heavy carpet over the entire door, overlapping the edges about 3 inches. The carpet should drag on the floor carpet. The carpet should be at least a half inch thick. You can use a few layers to get the thickness you need.
Unless you have a serious subwoofer in play, that should pretty much eliminate any problems. I wouldn't worry about the air vent. If that is a problem, you will need to hire a sheet metal company to come in and make a new duct that blocks the sound yet allows the air to flow.