First of all you are going to need something that states a local address like a phone bill or a water bill or an electricity bill (this is called the "comprobante de domocilio"). Since you don't live there, you will have to borrow one, and it doesn't matter if it is not in your name and if you don't live there. Without that, you won't be registering anything. The second absolutely necessary document is the "factura" or bill of sale. You need originals and a copy of both of these or you are going nowhere.
You will need your passport and your tourist visa (or your FM document if you have a number 2 or 3 type) for identification. It is quite a simple procedure, you show up with the paperwork and then you go to a bank to pay and then you return with the receipts stamped and they will give you your plate with a document that corresponds with it and also your "tarjeta de circulacion" which is your registration for the vehicle. You will get two documents, one for the plate and one for the bike, and the plate itself and don't lose any of these.
If you bought the bike at a dealer they likely have a "coyote" who you can pay to do pretty much everything for you. It is an easy process, just time consuming standing in line but the coyotes usually have a connection and move to the front of any line or hand the request to someone in the office that will do it quickly.
If the office you are registering it at is a busy one, they will probably have experience registering vehicles for foreigners. They will ask you for your "credencial electoral" which is the voter registration ID card that almost all Mexican adults have for universal identification in Mexico. You don't have one so you will use your FM tourist or resident document and your passport. This might confuse them unless they have worked with these documents before, but they will sort it out with a little time.
Don't go paying a fortune for this, the coyote should do it for less than $500 pesos maximum and if you have the time and the documents you can do it yourself, get there early in the morning and smile a lot. Don't listen to someone telling you that you can't do it because yes, you can get the registration. They might say that just to get some more money out of you. If you use a coyote, go with them because they will have your papers and a power of attorney that you have signed (carta de poder). I recommend you do it yourself.
The only difficult part is that it is boring. Even with the most basic Spanish it is not difficult, you just have to follow the bureaucratic procedures. It is also very likely that if you are not pushy and not loud, someone in the office will spend some time with you and help you and they probably will speak enough English to get you through it.
It is Mexico, and you generally will find someone around to help you out.
Don't even think about riding a bike that size on any toll highway, stick to rural roads and stay off the highways. Stay well to the right, way over on the shoulder if you do have to go on a highway. That bike will do about 80kmh flat out with you and luggage and it will take a long time to get to that speed. Also, those little bikes are among the most stolen in Mexico so get a good lock for it and keep it safe or it will disappear fast. Big bikes are rarely stolen, it is the delivery models that get ripped off all the time.