Welcome Simon.
Has your B2A got an XLR out as well as the standard jack socket? If so, that will send a clean signal to the input device. I'm told that a lot of studios had these just for recording.
For an active bass the output isn't huge, I agree. Did you check the volume trim pot in the pre? I can't imagine anyone wanting to reduce the output for a minute but it might be worth checking it out. Check your pickup heights too.
Also, these respond particularly well to light gauge, piano wound strings. You might find it difficult to get piano wound now. If you do, you may need a string clamp because double ball ends add another highly specific requirement. When slap was a significant cult, they were plentiful though.