I used to do the same, as a kid (not sure why my folks let me; probably a case of, "At least she's washing the car so we don't have to!") Since then, though, washing my own vehicles I only use stuff formulated for washing vehicles. No need for any of the extras that get dumped into liquid dish detergent (skin softening agents, extra grease cutting agents, etc.) and need something gentle that won't undo or prematurely remove all the waxing work I've done.

For the record, I got my Ford Escape Hybrid on March 6, 2006 and didn't wax it until the first week of June. I meant to have a little delay before its first wax (preceded by the clay bar) but didn't mean for it to be three MONTHS... just how it worked out with life and schedule at the time. A month is probably sufficient curing time, especially if you're in the southern U.S. (hot, hot, hot summer brewing; doesn't bode well for hurricane season.)