So the question that begs to be asked is "if you're a virgin and going solo" won't you still be a virgin afterwards?
I think your timing is pretty good but northern Mexico can still be pretty cold at that time of the year, especially at higher elevations. I saw snow on the mountain peaks in Sonora state in early March in 2010 and ended up using my heated vest for a day. There was frost on cars in the morning and on my tent at Creel (about 7000' elevation) But you should be able to put some distance behind you very quickly, especially if you're willing to take the toll highways to get further south in a hurry.
Depending on how long you're going for that might be a good time to avoid the rainy season in Central America. That usually comes around in early May ...give or take.
Have a blast on your trip!!