Thing to keep in mind (I have a 12 year old doing this now)-
GROWTH SPURT!!!
She's grown 3" this past year...

Also, I was 4'8", 66lbs at the beginning of 6th grade. At the end of 8th grade I was 5'8".
Ma could have shot me for all the clothes I went through! We did get my bike (a Flandria) from a garage sale for $60. That's very hit or miss. It was a little too big at first but I very quickly grew into it.

Best of luck finding a decent bike for cheap!