If you have a month in Baja, you will want a dual sport bike. There are more fingers on both your hands than there are highways in Baja. The real jewels are off the beaten path - not paved.
Assuming: You're flying in, have 30 days, want to see all you can, not be limited by rental/hire restrictions, not be limited by the type of bikes available for rent/hire, want the freedom to move at your own pace...and some other good stuff.
What I would do is contact some dealers in the San Diego area and arrange to purchase a very late model, low mileage dual sport bike that would fit your needs. Say...400-650cc, well prepped, excellent condition.
Ride towards your dreams for a month and sell it back to them for $1000-1500 less than you paid for it. They would more than likely provide airport transfers for you.
It shouldn't be too difficult to find a dealer for such a plan, with conditions, of course. They make $, you get a reliable bike that you like and have a cheap vacation.
Also, a benefit to 30 days are the permanent registration/tag requirements that you will avoid.
TJ and Mexicali (to a lesser degree) feed the north, business-wise/parts/imports. La Paz and Santa Rosalia feed the south.