It’s a tough one to try and think of an off road route to Lee Quarry from Bolton. There are quite a few rough/farm tracks from Rammy up to Rooley Moor Road via Edenfield but nothing really direct to Lee Quarry.
If you by-pass Rammy to the north and go via Edgworth, you get stuck having to ride (legally) on road pretty much from Haslingden to Bacup. There is an off road route from the back of the ski slope in Rawtenstall to Waterfoot, but it’s about 10 miles compared to 3 on the road.
I’ve also remembered that there is a bridleway from Edgworth to Rammy round Holcombe Hill. It goes round the back of the TA Training camp where they used to hold the original Krypton Factor assault course.
There are a couple of leaflets available free from Lancashire County Council that list a few routes round Rawtenstall and some in the forest of Bowland.