A player should be consistent about always playing in contact lenses or always playing in glasses. Switching from one to the other, objects 4 feet away (like maybe where the tennis ball is when you hit it) can seem shifted by a couple of inches or more. Also glasses make objects appear smaller or larger--let's say a nearsighted player used to playing in contact lenses goes out to play in glasses instead, the ball will look smaller, so he'll think it's farther away than it really is. He'll also have trouble finding his sweetspot due to the image position shifting.
As far as different types of contact lenses go, you're in the best position to know what works for you. If you felt like you saw the ball better and played better in non-bifocal contact lenses that you previously wore, that tells you something. It's not that big a deal to change out contact lenses for tennis, we all do a lot weirder stuff than that "for the love of the game."
You raise an interesting points about the eyes and brain adapting to either glasses or contacts, and switching back and forth may upset your judgement of distance, and hence timing.
I wonder if taking off glasses and putting in contacts right before playing can require an adjustment. Or if you do this frequently, does the eye/brain instantly adjust?
As for the OP's initial question, I guess the best test is to get a pair of single vision contacts and decide for yourself. The "disposable" single vision contacts should not be that expensive.
There are now several different types of bifocal contact lenses. And it seems to me that the ball moves too rapidly to do the head tiling to keep it in focus with either the aspheric, concentric or tranlating designs, so that the single vision contact would work best.
But I would love to hear from other TT members who wear contacts.