I wonder if the killer knew that JJ was dead? could such a person hang around for long enough to find out? this would add to the other apparent risks (time, witnesses etc).
There could have been more than one killer.
If a bicycle was used, it would be very obvious unless the bridleway was regularly used by cyclists, and if it was a rough track it could be mostly enthusiasts dressed for the sport? so everyday clothing and type of bicycle would be noticed?
There is also the possibility of tyre tracks being found, and who would risk the possibility of a puncture?
It occurs to me that if you start to bludgeon someone over the head in a regularly used public place, you need to stop very quickly in case someone happens along (cyclists included as they can appear very quickly) so, depending on your intention, I think you would either hit them gently and carefully to frighten them, then run, leaving them able to identify you, or put all your strength into ensuring that the minimum time and blows would kill them, and to do the latter, what experience would you be calling on?