Tons of adults have Twitter accounts. On OOTB alone, I know gtee, myself, 71, RH, and heelman all have Twitter.
I think Bieber has more fans from a broader age group than you think. Keep in mind that people (sure, a lot are girls) who were 17-18 when he first came out, are now in their mid or even late 20s. I'm not trying to argue necessarily, I'm just playing Devil's advocate. To me, it's interesting how certain celebs because a lightning rod for hatred and everyone immediately just says "Oh, I hate [so and so]" and it becomes the 'cool' thing to do. Groupthink has always bothered me, so I like to challenge it whenever I see it.