A bit of this information is going to depend on the age of your particular "V". They have been making them for a very long time, with only minor revisions to the design over the decades - unfortunately, those revisions can be a make it or break it deal with some of them. Bubbles in the cup, or paint backing up into the brush on a Paasche V is almost always the lack of a seal at the base of the nozzle cone in the brush body. When I assemble these pieces I generally use some sort of a sealing material in a few areas - for most of this, normal, everyday chapstick will work wonders. I start by slipping the nozzle onto a toothpick, and applying a small amount of wax (chapstick) around the lower portion of the taper on the nozzle that will fit into the brush body.
After placing the nozzle into the taper in the body, and checking that not too much wax will squish out, I then apply some to the threads of the nozzle cap. If there is going to be a good bit of squish out, or if it looks like the air passages may get blocked, I use the tip of a toothpick to clean things off before proceeding.
Same goes for the air cap - a light smear of wax onto the threads before installing it.
I assemble the parts and snug them up, but do not go overboard tightening. The wax should deal with creating a good seal on each of the parts. I test to see if I was successful by drizzling soapy water over the joints while releasing air - no bubbles should form if I did a good job sealing. Bubbles or foam will appear in the joints if I missed...
The head parts are generally marked with some sort of a line to indicate size. The base nozzle cap is the same between sizes, but the air caps have either one line, or two on them. These should correspond with your cone, and your needle. In addition, over the years they made changes to the specs on some of these parts, so it is better to try changing them as a complete set of parts, rather than mixing and matching. I have had a hard time getting the newer #1's to work on older brushes, as the air cap will sometimes completely shut off the air flow through the head. I have, however been fortunate enough to find new/old stock on many of the older pieces to keep my older "V's" singing along in style. The number 2 sets seem to work more readily on older brushes.