You can register a bicycle. You just need to do it in a pretty intricate and complex way. There's a couple ways to go about it after I researched various forums, sites, and people who got PA plates on their motorized bikes. I even talked to enhanced inspection station personnel.
The first way of going about it, would be to take it down to an EIS and reg it as a specially constructed vehicle. This appears to be a little lengthy way of going about it, and costly, but it works.
The other way, would be to never consider your MB an MB, and to just look at it as a MOPED. You then either go to the DMV with a notarized bill of sale (get a friend to do this or whatever) with the VIN as the S/N on the frame, and then never mention it as a bicycle with a motor. This is IMPORTANT it seems. Because if you say "Motorized bicycle" you are going to confuse them and or make them question you. Always refer to it as a MOPED. It's a MOPED. That's what it is defined as under the law, and don't let them think any different. If you say anything else you will then have to define everything, which is too much of a hassle they won't bother with. So just refer to it as a MOPED.
You could also try this out of state in a state that accepts this if PA fails, then just transfer the registration. E.g. Vermont for example. Vermont is pretty lenient, they really don't care much as long as they get their pay. And they will title the MOPED for you.
So all in all, it really depends which route you're trying to go down. From what I've seen, doing the "specially constructed vehicle" route just seem like too much of a hassle. So just try to play it off as a MOPED. I mean, it IS A MOPED, the definition fits. The law fits. You just don't have a title. So just circumvent that by going through another way