Bummer that sure is a hindrance
Been doing that here in XXX for nearly a year. Many people shout online and on forums such as this one about how dangerous it is citing bad experiences they've had and how stupid people are to do it.
Well, my take on it is that when I see how they were doing it, I know who the stupid ones are.
The way I do it safely is:
1) I never hold the lead in the hand or on the wrist. You cannot steer effectively in the case that the dog pulls due to a distraction.
2) I have a small 16" wheel cycle and I tether the lead as low down as possible, on the chain stay or low down on the rear carrier. This way the pulling force moment is comparatively low. On the odd occasion when he does get distracted (very rare these days) he absolutely cannot pull me over... and he's a very strong dog.
It's as if he is pulling the rear wheel sideways from near ground level... which with someone sitting on the bike is virtually impossible. The higher the tether point, the more the chance of being pulled over.
3) I tether the dog on the LHS of the cycle... so if on the road the dog is kerbside away from traffic. The lead length is short so he cannot run in front of the front wheel. his nose can only get abeam the front wheel axle point. Include a short length of ocky strap stuff as a bit of a shock-absorber if you like, You need to play around with this to get the length just right.
4) The dog must be trained appropriately. a good 'heel', pulling is ok unless we are approaching a junction or roundabout... when he should respond to 'slowdown' or 'wait'.... and a good 'look' command. usually after his initial burst of pent up energy he'll settle down to just staying alongside, neither pulling nor dragging. Make sure your brakes are always well adjusted.
5) Rarely break into a run except for the initial 50 metres to let off some steam... at which point we settle down to his fast or medium walk gait. Never push him past his limits... if you know your dog you'll know when.
6) Always carry water bottles and vessel for dog to take a drink. have a rest if he's very tired. i never go more than about 3km each way tops.
7) Stop at favourite trees/posts etc
8) I always keep a good lookout for dogs/cats/rabbits etc and take avoidance action if you feel it's necessary... talk to the dog if required so he knows you're onto it... andr be prepared for a possible tug. Stop if you feel you have to until the distraction passes.
9) I sometimes use the footpath if few people are using it... or alternatively the road. If on footpath am always considerate of other users and go slowly ringing my bell if required to give a timely warning. People invariably look around and give way if it's a narrow path. I thank them... and everyone's happy.
Most people smile and see a happy well exercised dog loving his walkies. But there are always those holier than thou arseholes walking around telling you how to live your life and how stupid i am.
PS, if I were to use my normal roadster bicycle to do this (which I never have had to do) I would manufacture a steel down bracket from the chain stay whose end would be about 250mm from the ground with a tethering point at it's end. Some kind of triangulation for rigidity would be incorporated.