That's what I thought.

A few things for the other poster, how are you going to qualify for the transfer of tourist to FM-3? Unless you have a job or a pension or can prove a healthy bank balance you might not get it. You will have to qualify as either a rentista (renter on a pension or renter with enough funds to qualify as not likely to run out of money) or a worker (you need a formal job offer and you will need a number of extra documents and have them apostilized as well), or you can qualify as a property owner if you have bought a house or a condo and have the legal title to it in your name. Time has nothing to do with qualifying for an FM-3, it all has to do with meeting the requirements and you can qualify from abroad through a Mexican consulate or embassy if you have everything in order. Just waiting out your tourist visa in Mexico and then asking for an FM-3 without qualifying for it will not get you very far.
Second, to register your bike you will have to import it. That means paying taxes etc... and the use of a good customs agent if they will handle this and many do not want the hassles and time involved.
Third, you will then need to plate it somewhere and begin to pay the yearly registration fees.
Unless you speak and write Spanish fairly well, you are likely going to need some professional assistance in this and it could get more costly than you think.
Just some things to consider. Remember, you can't always bribe every official even though it is Mexico. Think through what you are planning on doing and figure on a cost and then double that in time and money.
That will put you in the ball park.