I'm 5'6 and a bit would a 21' bmx bike be too big for me?
A bit, but you won't die.
You'd probably find a 20.5 or 20.75" frame to be a little bit more maneuverable.
Chris
www.bmxtransition.com
Canadian BMX Mailorder
Instagram: @transitionbmx
Personal preference but I think 20.5-20.8 would be better. I'm a few inches taller and I hated 21" tt.
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You can try it out on a friends bike or something but I wouldn't recommend buying a new frame to try it.
If I were you, I would get something between 20.25 and 20.8 as said above. It's all up to you though.
If you can, try out a couple of your friend's bikes and see what you like the most.