I was really nervous to ask for them too. My conversation when something like:
Me: (Really nervous) I'm applying to vet school this cycle, blah blah... Would you be willing to write--
Vets: (big smile) Of course!
Email does help. I was really nervous asking a professor for a letter, because I'm at a big school and made the mistake of not getting to know my professors, so I expected they would say no. It was easier to ask over email and they said yes anyway.
Also, I asked around this month, if not earlier, last year. I just told people that VMCAS wouldn't open until June, and then I emailed the link to VMCAS in June along with a nice reminder and a thank you. My evaluators were happy with the way I handled it and said they appreciated having plenty of time to do it.
Good luck!