Soaking, Timing, and Chemical Baths
At home, the soaking time is not a science. As long as the bath water is not hot and the soap is not aggressive, it won't damage the metals. Wooden and synthetic parts may be harmed, though. I avoid leaving my instrument in water for too long because my slide cork is an actual cork (wooden). I shoot for about ten or twenty minutes.
During the spare few minutes, prepare the bell section for cleaning and pull out oils and greases for post-cleaning maintenance.
My understanding is that maintenance shops provide special chemical baths as a service completely different to the gentle sort of home-cleaning described here. Strong chemical baths are another important, yearly tradition, and help remove corrosion that gradually reduces the life of an instrument and eats the metal from the inside out. Trying to do a chemical bath at home is probably a royally bad idea, though. Accidentally making a bath full of poisonous chemical goo is ... well, you get the idea. Find a good shop if you'd like that done.

