Avoid letting Bowser make more than three full rotations before throwing him; afterwards, he will spin too fast and become more difficult to aim.
In order to trigger the text after Bowser is defeated, Mario must be facing towards and be within a short distance of him.
The "whoosh" sound that plays while spinning Bowser plays when he faces north, and is not indicative of whether he is pointing towards a bomb. Try to focus more on aiming visually.
It is highly recommended that runners who play using the original Nintendo 64 controller switch to a different controller for Bowser fights, as rapidly spinning the N64 controller's stick will wear it down. Recommended controllers include the Hori Pad Mini, a Retro-Bit Tribute 64, or a GameCube controller via a Raphnet adapter.
Bowser in the Dark World
Standard
To avoid an air throw, let the stick go neutral right before pressing B to throw.
In this battle, Mario cannot grab Bowser until the platform stops teetering. Avoid groundpounding around Bowser's side of the platform during this period, otherwise Mario may clip through and fall into the lava underneath.