A clean boost would give you an accompanying volume boost which might be a bit unmanageable playing live, so I'd go for a drive pedal personally, one that's fairly transparent that could be dialled back to a clean boost.
A TC Spark Booster would fit the bill, I've been meaning to try one as it's getting a rep as a fine bass overdrive in its own right, but the toggle switch lets you just use it as a boost pedal also. The Earthquaker Westwood is a new 'transparent overdrive' pedal out that also looks good, but really there are tons of low-gain bass-friendly overdrives out there, prepare to be overwhelmed with recommendations (both good and bad)!
Another recommendation that's slightly unusual is to use a dirty compressor like the Fairfield Accountant.