As you describe it the pistols are the most likely way to win. They have all of the advantages of the bikes without the disadvantages - in that they fire a lasting line with directional aiming rather than having to follow the path of your bike.
I'd aim to get ahead of my opponent and then fire the pistol left or right depending on which side they were on. No ...
Well, this is difficult without knowing the:
Size of the bikes
Speed/acceleration of the bikes
Size of the sphere
Do the lines of death affect dismounted humans? (eg. can someone get off their bike and run around shooting people, ignoring the lines of death?)
What happens if the bikes ram each other?
If you hit a line and die, will your generator still keep ...
Park bike. Lean it against line generator. You might turn line generator on its side.
Shelter beneath the 2 machines.
Make use of infinite ammo and start shooting. Your opponents will also be hiding under their machines so it will take a while for the match to be over.
Play loud rocking music so spectators don't get bored.