I'll be honest--I haven't played a Meta Knight in a long time, but I think that there isn't that great a risk in having your bike out (people need to get used to SDI-ing as many A attacks of Meta Knight's as possible to minimize damage and bad positioning). Wario has a pretty usable recovery even without his bike, due to his amazing horizontal aerial mobility and airdodges to the ground being so safe for him and in general. Even if we don't have our bike, we have a better recovery against Meta Knight than most characters.
Given that many of Meta Knight's attacks are multi-hit moves, hitlag from attacking the bike would probably give us a little more leeway. I believe his shorthop aerials cleanly avoid hitting a grounded bike, but, depending on his positioning, his options may be limited. An F-Tilt command will make him pick up the bike, and D-Tilt/D-Smash/F-Smash/Shuttle Loop will have some hitlag, potentially allowing us to punish where we could not in a normal situation.
After a shorthop F-Air, if we run in, roughly half of his go-to options are easier to punish if you guess correctly (or react to his F-Smash grunt and airdodge straight through him); much better to have to guess once rather than twice. He still has more than enough to play with us pretty easily, but, it does put pressure on his choices. His unaffected options are his rolls, spotdodge, shorthop aerials (especially U-Air), and grab options, most of which he puts himself out with no hitbox to attack with. Oh, and, Mach Tornado, but, **** Meta Knight.
For all it's worth, the "throwing the bike up with your back turned" thing works well against Meta Knight, due to his burning desire to running grab you when you pick up the bike, which gives you a gimmicky bait against people who don't know any better and a decent mix-up of "he can still throw it down or forward to hurt my other options" against people who are wary of the bait situation. This allows you to get damage on the bike while being far from helpless (though still not a good situation if the opponent knows what is safe). I wonder if throwing the bike upward with your back turned can stuff Mach Tornado, too...
The thing is, part of why we lose so badly to Meta Knight is because he has an absurd amount of options that we can't do anything about unless we make, like, two hard reads in advance. His character design just works really well in defending against Wario. The stuff listed above gives us a chance to weaken/negate some options to make it somewhat more reasonable.
As for tires, sure, he can't destroy them with his A attacks, but he has a stupid amount of speed, small size, and some fantastic B moves for getting rid of them. The biggest immediate advantages are protecting ourselves when above Meta Knight, like Toon Link does with his bombs, being able to reliably punish Mach Tornado and Shuttle Loop (as far as I can tell), and getting free damage on his shorthop aerials (though I'm not sure if we can do it on reaction, since Wario's item throw is slow). Anything that limits Meta Knight's safeness is useful in my book.
We also get to put him into sense paralysis, as his ridiculous wall of pokes cannot be thrown out freely, unless he doesn't mind risking extra damage. Of course, nothing stops him from catching the tires or instant throwing back if he isn't doing shorthop aerials, but, just getting him to have to think about what options he must do is helpful in itself, as Wario is all about pressure.
Also, to be fair, even if Meta Knight gets a tire, he can't do much with it to disrupt our general game plan. If we have another bike on the stage, his tire will bounce off harmlessly, unless he throws it from the air, which is easily caught/instant thrown/whatever.
Hunger you and Ally were my inspiration!
