I’ve reviewed my doorbell footage and our lot seem to just pull them by the handle straight to the back of the lorry, so handle out is definitely easier for them. I didn’t see anyone checking in the bin.
Edit: On further review, the bins go into the mechanism at the back of the lorry with the handle out (ie, they push them from behind into the lifter), so it might actually be easiest to have the bin sideways with the handle facing towards them as they walk down the street. That way they can just walk up to it and start pushing it towards the lorry.