If you are washing your vehicle by hand or at a “touchless” automatic wash then there should be no need to do anything with an antenna that does not stick out excessively; weatherproofing should be part of proper mounting.
If you need to take down the antenna, then how you do it will depend on the exact construction of your antenna and mount. If you're using an antenna which mounts to a 3/8"-24 stud, for example, then you can just remove the antenna, wash, and reinstall (after drying the joint). Even if the antenna is a type with a coaxial mount (e.g. NMO, PL-259) then there is a good chance there is some way to unscrew the whip portion.
However, you should be careful about leaving exposed any type of coaxial connection (as opposed to a stud or threaded hole). Unless specified otherwise, you should not assume that the insulator between the center and shield is weatherproof, and if it gets wet it may carry water into the coaxial cable which causes permanent damage.
If you can easily remove the entire mount with all connections intact, then you could just lay it down in your truck bed.
You will likely have an exposed coaxial connector between your mount and the feed line to your radio. This connection does need to be weatherproofed in most cases. (N connectors are designed to be weatherproof, but I would not rely solely on that.)
There is a specific type of tape which you use for this purpose — called variously “rubber tape”, “self-fusing tape”, “amalgamating tape”, “Coax Seal” (that being a brand name). It has the property of fusing to itself when stretched and pressed together, so that after application you do not have just layers of tape stuck together with adhesive, but rather a tightly fitting custom rubber boot, and when cut off afterward it leaves no residue and a pristine unweathered surface.
I personally have used 3M Temflex 2155 Rubber Splicing Tape for this and many other applications, and would highly recommend it.
Just remember that you have to stretch the tape as you wrap it.