I don't know if this helps or not to reduce the time, maybe you know it and it doesn't help. You don't have to fight Bowser every single time, if you get an INSIGNIE right when he/it appears, he/it leaves and you actually damage him/it (meaning, instead of fighting you just grab the Insignie). Later, when you HAVE to fight it (him?) you face it/him but he doesn't have all his/its HP, and thus the battle is a shorter one. My kids fought him this way. I hope it helps. Congrats.
That wouldn’t help in this category. Once you damage Bowser with a shine, you have to wait another 3 and a half minutes for him to come back to damage him again or enter the giga bell. Skipping one boss fight would take multiple of these waiting periods, so it wouldn’t save time. This is used in the Any% Amiibo record though since they can bypass the 3:30 waiting section with the Bowser Amiibo.