The fastest way, by far, to grow your Twitter account is to automate it. I use Twitter quite a lot for prospecting. I currently have 9 Twitter accounts and, at the time of this writing, acquire about 300 new followers total per day. That's not so many but I keep it conservative to avoid attracting Twitter's attention.
Try to stay under Twitter's radar by not being too aggressive in acquiring new followers. Twitter will suspend accounts if any of its limits are breached. It is now becoming harder and harder to get a suspended account reinstated. The larger of a Twitter following you have, the more you have to lose if Twitter suspends one or more of your accounts.
Wish u good luck.