A simple google search turned up this shop
. Renting a bass is the way to go. If you go and buy a "budget" bass somewhere, you're most likely to find a BSO (bass-shaped object) that's nearly impossible even for a professional to play properly. The setup and ease of playability is crucial
here otherwise your kid can be injured
. Just as bad, he could lose interest because it physically hurts to play. Then you're stuck with an instrument to sell. Look for a rental/purchase kind of contract so that if you decide to purchase a good instrument later on, you have some equity to work with from your rental history.
On an unrelated note, think of the initial hefty expense as an investment. If your kid really gets into it, he has something to keep him busy and away from the bad influences that plague kids his age. In addition, the competition for bass players isn't nearly as cut-throat as it is for violinists. College scholarships can be easier to obtain. At some colleges he could play in the university symphony to meet his scholarship requirements and major in something unrelated to music!
The world needs more bassists, do your part! and good luck!