I've got a Black Lab that rides with me all the time. I live in Essex, County Ontario, about an hour from Ann Arbor.
When I'm on something like Rail Trails with the dog and I see an oncoming cyclist, I either leash him or just stop and have the dog sit beside me until the cyclist goes buy (he's a very well behaved dog and doesn't chase)
When I hit the trails, he diligently follows me. Whenever we come upon a cyclist, I'll just momentarily stop, the dog sits by my side, I hold his collar (more for satisfying the cyclist than for the dog) and let the cyclist pass.
Funny story with the Lab. The first time we went to a nearby MTB park, we went through and he had a blast following me. There are some sections where the single track zig-zags back and forth. The second time we came upon the zig zag sections, he'd stop at the beginning and watch me go back and forth. Then, when I was all done, he would just skip over the zig zags in a straight line saving himself all those extra steps.
Canflyboy