Bullet Level
Bullet Level is the strength of your current firepower. At the start of a new game this is 1 (unless you have unlocked the Power Up talent, in which case you can start the game with anything up to Bullet Level 5). On some ships, such as Pulse Blast, the bullet level is simply the number of bullets fired out at any time. On other ships, such as Terminator, the firepower simply becomes more powerful.
Upgrading
On any ship, the maximum Bullet Level starts off at 8. You can upgrade the Bullet Level a further 8 times, giving that ship a maximum Bullet Level of 16. The cost for each upgrade becomes higher for each subsequent upgrade. Details of these can be found on the individual ship pages.
If you collect a Super Power, it will set your ship to a Bullet Level of 17.