I've been playing brass for over thirty years - I bathe it about once a year (if I remember) - never had any problems.
Dead easy to do - pour warm soapy water down the bell (just a couple of drops of washing up liquid is enough - you don't want loads of suds) and and keep pouring until the water comes out of the mouthpipe.
Work the valves whilst you do it. Repeat. Then repeat with cold clear water a couple of times to rinse out ALL the soap.
(You can do all this by completely immersing the instrument in the bath - I don't)
It might be worth then oiling the valves with a little "VALVE" oil - it should say "valve oil" on the bottle - if it doesn't, it may not be suitable. If it has a picture of a trombone on the bottle it almost certainly isn't.
Pull out the slides to empty them and clean the legs, then grease them lightly with slide cream - (trombone slide cream is different stuff)
Only put a tiny bit of oil on the valves - too much and it could make them sluggish.
Be careful how you press the valves down when you're playing - make sure they go down straight. The vast majority of valve sticking problems stem from players pressing down the valves at a slight angle.
All the best,