A child needs to be at least in the 5th grade to take string bass lessons.
It is not necessary to be tall to play the string bass.
Several stores in our area have excellent rent-to-own programs for string instruments. We recommend The Violin Shoppe http://www.theviolinshoppe.net and Davidson Violins with several locations in the area http://www.davidsonviolins.com
For purchasing a string bass we recommend the Bass Violin Shop in Greensboro, NC. http://bassviolinshop.com