I recently started a new blog but was kind of worrying about how I would grow my associated Twitter. I knew that I could "boost" my Facebook page, but Twitter doesn't allow brand new users to advertise their profile.
Anyways, I managed to get 250 followers in 2 days really easily. Basically, I just followed other people in the niche. I followed people that Twitter suggested under "Who to Follow" (if they were in the same niche).
I also searched keywords and hashtags in my niche and followed people who showed up in the results. I am following 575 users, and have 251 followers. Roughly 1 follower for every person I followed.
I'm sure this isn't news to any of you, it may come off as a real newbie post, but I thought I'd share in case someone else got value out of it.
**Pro-Tip: Don't just follow everyone Twitter suggests. I did that at first and ended up accidentally following some pretty extreme political and religious groups by accident . It messed up all my "Who to Follow." I had to manually unfollow them afterwards, which took a little while haha.