How about get up at 0530hr, cycle 9 miles to work, have a quick shower, work till 12ish wash using soap and a flannel, work till 1900hrs, cycle home, have a quick shower, eat tea. Chill with the family, get ready for bed about 2230hrs wash with a flannel and soap and brush teeth, and go to bed.
A small hand towel, a flannel and a small bar of soap in a waterproof toilet bag, add a few baby wipes for places that don't have warm water to wash in.
We are all but limited only by our imagination.