Hey Jenn,
I started riding with my golden retriever back in NJ when she was only 3 months old and she picked it up naturally. Since then I have had a bunch of other trail dogs and they have all been naturals. I have 2 dogs that ride right now, both were adopted as adults and just took to it naturally. It is different then running where they are naturally way faster than you, here they need to actually work too. One is a pit mix and stays glued to my tire, the other is a bisenji/lab mix who is a little more fun. She will run alongside the trail instead of on the trail whenever she can, she is very polite and always yields. I put a cowbell on someones collar when i take dogs, so riders won't come head on and hurt themselves or my girls. Once at Boyette, we caught up with some guys and someone said he could here us clanging for a long time and was sure someone broke a bike or something. I have thrown myself down a couple times avoiding my own dogs, usually in a tech situation so you rarely worry about it down here in FL. I also had an episode where my dog hesitated going over a wood bridge and caused someone in my group to go down. Luckily for me, all my bros seem to love having the dogs as part of the group so it was no issue, we all laughed. If you are the type to take your dog to the beach(LOOOVE FT DESOTO!!) then you will probably like letting your mutt go for a run on the trails.
I find ill behaved dogs on the trail no more annoying then slow kids or even slower parents, everyone can enjoy the woods, just be nice.
erik