As I understand them, there are some connotations that you might not know as a learner. I have provided pictures of what they could mean, without further context.
(Short for mountain biking.) I think there is also the possibility of understanding biking to mean riding motorcycles, the Harley-Davidson types.
This is what I personally imagine: casual, roadside riding.
Ride bikes. Often means 3, but can also mean motorcycle riding.
(Motorcycles are sometimes called bikes.)
Now 1-4 are what I imagine without context. I suspect you mean something along the lines of 3. So if your audience expects bike-riding, like in 3, then I believe using "Let’s go biking/ride bicycles/ride bikes." should all work fine.
I think I would personally say "Let's go bike-riding." Again, it could mean motorcycle, but if your audience expects something like 3, then it should work fine. Bicycle-riding works too.