Hi

I've bike with my dog running beside me loose, on a leash, on a mount attached to the bike and in a trailer. In addition, I have an all-terrain scooter which I attach my dog to using an X-back harness. My dog is a Vizsla - so plenty big enough & athletic enough to keep up with the bike.

I know dachsie's aren't lap dogs - but I really think the dog is far far too small to keep up with even the slowest bike (although no doubt it will try its heart out!) I would invest in either a really good basket for the front (which has a cage over the top to stop the dog escaping - Rixen Kaul make very good ones) - or a dog trailer. Doggy Ride is excellent - I have the large size, but obviously the small size would be perfect. It also doubles as a great load carrier. I can't say my dog loves the trailer yet - but she is tied down pretty tight to stop her jumping out. She has her head out the top which works pretty well. It's a great way to take your dog with you and certainly turns heads (we cycle round the middle of London with her head poking out the top & ears flying in the wind!!) Another thought is to put your dog in a backpack. I have no experience of this - but there's a great video (maybe on YouTube) about a guy who describes exactly how to do it safely.