IMO, I think he dumped her body {sorry, hate that term, but you know} in the early A.M.,...........just BEFORE he stopped off for laundry detergent. He went home, began wash,....Nancy's clothes? towels? I dunno!
I think he maybe needed milk and juice so ran to the store really quick,....or he had to quickly dump off something that didn't come clean, dumpster? So he stopped off at the store.
IMO, there was a reason he didn't want anyone at the home before he left and came back, later in the day after talking to Nancy's friends. Or, well, maybe he was not ready to face any questions yet? OR....part of the 'staging' he knew he needed to LOOK for her before he sounded the alarm?
ONE of those is the reason he left the home and took the children and didn't want to see anyone until he came BACK from looking for Nancy.
Hmmmmm........be interesting to know IF he was in the vicinity where Nancy was eventually found, SHORTLY before he met LE at his home.
Kinda' like SP who kept driving by the Bay and stopping and looking out! Maybe Brad wanted to be sure she had NOT been found.
JMHO
fran
PS......IF there was blood, face it, he would NOT know how to get it out. He didn't have his MBA in laundry.