Bowl boosting (formerly known as bubble bowl boosting or BBB) is the process of dying such that Hans grabs SpongeBob, then using a bubble bowl on the first frame after Hans drops SpongeBob back into the game. This results in a considerable speed boost.
A bowl boost abuses the displacement properties of the bubble bowl move. This can be demonstrated by doing a standing bowl and then a bowl after moving. The bowl after moving goes much faster because there is displacement. Hans keeps your last position for 1 frame and doesn't update to the respawn position for another 1 frame. Because Hans putting you down keeps your last position, if you bowl on that 1 frame it counts as displacement from the previous position and gives you massive speed.
A bowl boost jump (BBJ) is a bowl boost, with the addition of jumping, to cover a larger gap than normal. With appropriate timing, this allows the player a range of movement throughout the map.