I tried this for years man it never amounted to anything significant
You need to either have the bunny at 1:25 in Level 5 (usually means getting 6 infinite mode achievements in under a minute, which is extremely hard and luck based), or unlocking bunny in Level 59, with the following achievements:
Dodge the Squares
A Breath of Fresh Nothing
Isn't that Cheating?
Galactic Vandalism
Keep it Simple
The Conscientious Lizard
A Bumpy Ride
Grinding the Tunnel (into dust)
Using the Bunny for only the last 5 levels of the run hardly saves any time. I haven't done enough testing with a 3 infinite achievement route (unlocking bunny after level 17) but from what attempts I did in 2022 I didn't get much success with that route either.
The current route in Any% still has at least 3 seconds to save to just menus, and I feel those are much easier to shave off than using Bunny routes. The 0.7-1.5 seconds lost just to switch to bunny matter tremendously at this level already. Bunny routes have been theorized for years now and nothing has come of them. Sorry, but I really don't think the Bunny will find its way into Any% anytime soon. :((