In my opinion it's easier to start a virtual bookkeeping business after you've already started a local business. (Not to say it's not possible to start virtual first, but...) With that said, there are some differences in being local vs. being virtual. Before you start looking into that market be sure you have the answers to the questions you're going to get: How can you do it? There are some threads on here on how to access your client's records,
this one is pretty informative. You'll also want to have in place how you'll get your client's records (e-mail, fax, ftp, mail, etc.).
How long it takes depends on how much you market yourself. There's no answer to that. If you are currently going on-site for your clients see if any of them are willing to go virtual. It saved my on-site clients money when they let me go virtual -- they didn't have to pay for travel time or my on-site premium.
Good luck! Be sure to read through all the threads in this section, there's a lot of great information here.