Step 1 - I would bring the bike inside overnight to warm it up, take the bike and a bucket of hot soapy water outside the next morning and scrub that thing down once quickly.
Step 2 - Then I would put generous amounts of lube all over everything and be done with it.
Alternmate Step 2 - If you really wanted to do the detail cleaning, at least you'd have a good chung of the grime off before you started soiling up your tub. The thick globs of grease, grime, road salt, dirt etc. will clog up your drain right quick if you don't get most of it off first. But the tub will work - be prepared for a b!tch of a time getting grease smudges off the porcelain. Oh, if you have a plastic surface on your tub, forget it.