I am not very horsey although I have some riding experience, but I am a farmer in a very rural area. If the scenario is that three people need to make an urgent journey and the transport available is horses plus a bike, and one of the people has no riding experience, then I would think it more likely that they would take three horses and just have the horse for the inexperienced person on a leading rein. Especially if the journey is likely to be at horse walking pace, not requiring gaits that are harder for an inexperienced person. A combined horse/bicycle group is going to be much more inherently awkward for reasons others have discussed.

Of course if you want it to be the bicycle for plot reasons there's no reason you shouldn't, but personally I find three horses more likely.

Also, I would be surprised that the roads are lit in a rural area without many cars, they are not lit where I live aside from the bits where they pass through villages. But again perhaps your worldbuilding accounts for that :)