Brief background----
Played bass for two years at church. Played a MIM Fender Jazz through a GK Backline ---. Throughout the years of playing, driving the 8th notes sounded good, pretty smooth, etc etc. I then stopped playing for 3 years to pick up the guitar after friends needed a guitar player. Now I'm back to my roots playing my first love, the bass guitar!
But here's the problem. Playing live with a nice 18'' speaker pumping lows out like crazy, driving the 8ths even at a pretty fast tempo sounded great. It sounded smooth and not choppy. But now I'm playing through a Genz Benz Shuttle 9.0, and this amp is so much less forgiving than the GK that I used to play through. I've taken a shot at recording and it seems like those 8ths that I used to drive are no longer smooth. Every time I alternate, it feels like there is such a large gap between the time the note stops and starts ringing again. I've been trying to lay down a bass part for a recording for the past couple of days, but the DI from the Genz Benz has been kicking my butt

How do I smoothen out my alternating to give it a nice smooth transition from finger to finger?