Arguably, he COULD have, sans lights. He wouldn't have needed to go for many yards, on the main road, before taking a right turn and doing a detour cross country, using farm tracks.
Ainsley has him cycling along Maldon Road about a mile to the farm track that leads to Brook House Farm. That's still two miles in all that he cycled out on a public road on his way to and from a mass murder. Those two miles must have felt like 20. In addition, if Ainsley is right, this means Jeremy has cycled over rough farm and field tracks, again at night. You suggest he may have done this without lights.
Then there's the problem of how to get in and out of the environs of the cottage and Goldhanger without being seen. That's risky enough if just going on foot. The bike had a squeak when shown to Barbara Wilson a week or two before, but we'll err on the side of the prosecution and assume this had been sorted out. We'll also give the prosecution the benefit of the doubt and say that, on the public road, Jeremy could have worn dark clothing and a balaclava under a hood, and on seeing a car, he could have put his head down and taken other simple precautions. The only risk he then takes is that someone later reports seeing a cyclist out in the middle of the night. Even if that happened, the witness would not be able to positively identify Jeremy.
Or would they? The fact is that even when someone is disguised, you can still identify them. Somebody may have recognised the bike or Jeremy's clothing. Not that such an identification would be reliable or assist the prosecution much, but here we are considering not the legal case, but the risk calculations that Jeremy might take. You would need only one driver, other road user, farmer or neighbour - anyone - to see him, and potentially, suspicion then falls on Jeremy and he faces questions and inquiries. People who plan things like this tend to do so with minimising risk in mind. A bicycle complicates things. It means noise. It can slow him down. It forces him to run into vehicles and maybe pedestrians who will all see him, albeit he may be disguised. What if a puncture or mechanical fault develops? Surely it's simpler and less risky to go by foot?