Dishwashing detergent is not a good idea on paint. It "takes away grease" from your dishes, which also means that is removes the petrolium content from your paint. It make paint go powdery and flat.

I have a bare Ti frame. So, Paint? I don't have no steeenkin' paint.

I usually do a wipe down with Windex every week or two. Once a month or so I clean the chain with a Park chain cleaner and give the cassette, chainrings and pulleys a scrub.

If it's really nasty, just wash it like a car. Just use low pressure to rinse. Towel dry. Give it a kiss. Relube the chain.