I come from a similar background in brass, but form the tenor horn section. Point one i will make is that because you have being using three fingers to play valves you are way ahead of the game as far a finger picking styles are concerned, so don't be scared to use 3 fingers as opposed to two, it never done me any harm and in many ways was gift to have it.
Tabs are a tool to use inconjunction with your playing, if they work for you go for it, don't let anyone tell you different.
But try re-apply what you know concerning theory and using you ears to the bass. Some of it will apply some of it won't. Don't try and deny your treble clef skills for the sake of bass cleff, run the two side by side..piano players do it.
That point is about application, that's the one mistake i made that wasted a lot of my time. I found it easier just to learn the bass clef rather than try and transpose the treble in to it. I know that may seem stange and i may be just the oppisite for you as most trumpet players i know transpose in their head sheets for Bb trumpet to Eb trumpet with out the blink of an eye.
If you have lots of Trumpet sheets turn them upside down and sight read them as bass clef, turn them back and sight read them a treble. If you feel brave even try and play then in the bass clef, you never know what you will find.LOL
Have fun and enjoy..welcome to the bass end of music LOL