Unless you're really slow, your dachsie won't be able to keep up. If you watch dogs running & playing, they'll go really fast, then stop & repeat. Not many breeds (herding breeds excepted) are made for running non-stop. Some sporting breeds seem to enjoy it - but in every case, I'd watch the surface they're running on (soft is better) and be mindful of skeletal issues.

Regarding a trailer, I'd spend lots of time with him in it & NOT hooked up to your bike. Put treats, his blanket & toys in it - make it a good thing. When he is comfortable with it, I'd manually move it just a little & see how he reacts. Patience is good. I'd hope that when he's finally hooked up, you'd have a restraining harness so he can't jump out.