On the motorbike you want to use mostly front brake. On the bicycle mostly rear. So having them both on the right bar makes sense to me, so you are always reflexively going for the correct brake in a panic.
It's a little more complicated like that, at least for bicycles. I trained, raced, and rode competitively for many years on bicycles. On a bicycle, both brakes are essentially the same design (if they are rim brakes), and have the same intrinsic ability to slow the pertinent wheel. On a bicycle, like a motorcycle, the weight shifts to the front as you slow. It's much easier to skid the rear wheel than on a motorcycle, which typically has a much weaker brake on the back. Like a motorcycle, skidding the front wheel is much more exciting than skidding the back. Since your own bodyweight is a far higher percentage of the total weight on a bicycle compared to a motorcycle, skidding the front is harder on a bicycle than on a MC. You're more likely to overturn the bike (highside) than you are to skid the front wheel. On the other hand, corrections you make instinctively via your bodyweight as you try to maintain balance are a lot more effective on a bicycle than a motorcycle.
Since you are training endlessly as a bicyclist, and you're always running into situations on the road, you eventually figure out the best way to brake and it becomes body memory. In a pack, when I had to dump a little speed in a hurry for some reason, I'd always use my front brake only (left hand). If I was alone and had to stop quickly, I'd use both brakes modulating appropriately.
I never had an issue confusing bicycle and MC reflexes. I think the different sensory experience of the bike and MC was enough to trigger the correct body memory responses.