The 85 is a straight-up DI, it won't handle the output of an amp. It goes between the bass and amp. Wrong - looking at the wrong product altogether
It sounds like what you're after is a preamp with some tonal control. If you nip over to the effects forum you'll find plenty of options mentioned. Nicest I've tried in a while is the Origin Effects Bassrig Super Vintage, which is Ampeg-flavoured, but they also do a Fender-flavoured one, the Bassrig '64. Sounds like it could be exactly what you're after. Quality items.
If you want the sound of your amp, you could consider something like the Two Notes Torpedo Captor which is a load box that goes between your amp and speaker cab and provides a DI output