| according to Arnold
This is from Arnold E Schnitzer's New Standard Chat site. I think it is a good guide line. I thought there was a sticky on this.
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Here are my basic measurements for those looking for some simple guidelines. All measurements are from the end of the fingerboard to the underside of the string. These are for metal strings.
General set-up: G string 5mm; E string 8mm
Orchestra set-up: 6mm; 9mm
Low Jazz: 4mm; 7mm
Hi Jazz/Heavy Orchestra: 7mm; 10mm
Gut strings:
Jazz: 9mm; 13mm
Slapper: 12mm; 16mm
The D and A string heights are dependent on the fingerboard arch. Ideally, the arch allows for 1mm extra clearance for each string; i.e., G5, D6, A7, E8. However, higher strings require more arch, and conversely, lower strings can use less arch. This all assumes the bass will be bowed. If not, the arch can be set up flatter. Some basses, like Kays, were built with very flat fingerboards, and may require more height on the middle strings, especially the D. | 
