Well the OP is based in Glasgow so he's not far from proper wilderness is he?
Basic common sense applies as in hill walking. Take suitable clothing based on where you route goes and sufficient water/food. Basic multi-tool, chain tool, spare tubes & pump. Make sure someone knows where you're going. If you don't have a sound knowledge of the area you're riding then an OS map (and compass) is useful.
If your ride may extend into the hours of darkness then offroad lights should be left on the bike or at least a headtorch taken along.
I guess the difference with biking is the greater likelihood of accidents. I do a lot of riding by myself and tend to throttle back to about 90% on fast downhills or tricky technical bits coz I know that if I come a cropper there's only the dog to help me.
Despite knowing all this I came to grief recently by ignoring several of the rules whilst riding in an unfamiliar place. 2 punctures and a mechanical put me way over schedule and darkness came down, then snow. Didn't have any lights or a map. Got totally lost and cold(ish). Eventually located a road by climbing down a gully and fording a river then hiking through a dense wood. Then figured out where I was and rode back to the car. The dog loved it though.....
On most of my rides I never see another soul - one of the beauties of living in the north of Scotland and one of the perils.