What I did, when I did it many years ago, was to countersink the tip of the bullet and then splay the individual strands of the wire out into the countersunk area. Then just heat the tip of the bullet, and the wires of course, and touch the solder wire to it. You will get a good connection but more importantly the bullet will stay on the wire when you pull it back out of the bullet receptor at any time.
If you have a lot of bullets to countersink you can hold the countersing bit in a vice and the bullet in a drill chuck. If you have the bullet tip flush with the chuck jaw tips you will get the depth that you need without ruining the bullet when the countersink bit snatches on the soft material of the bullet, as it will.
Trim the wire that you want to solder in place such that the outer plastic will fit inside the bullet when the inner wire only just protudes proud of the bullet tip. If the situation allows it, it can be very handy to lightly grip the wire and bullet with a pair of static Mole Grips, for example. Otherwise you will have a difficult job trying to hold the wire, solder and soldering iron all at the same time.
Good luck,
Angus