Bob Barker's Historic L.A. Estate Sells for Well Over Asking Price

Bob Barker's historic estate was listed for $2.9 million -- but whoever snapped it up ended up spending even more to buy it ... going well over asking.

Real estate sources tell TMZ ... interior designer Julia Dempster sealed the deal Thursday by plunking down a whopping $3,788,000 on the 6-bedroom, 6-bath Spanish Colonial Revival-style Hollywood Hills estate, this just a month after it hit the market.

We're told the estate had a staggering 250 showings, so it was clearly in high demand ... hence why Julia had to dig deep into her pockets to snag it. Now, she gets to sit back, relax and enjoy her new home, which is a true slice of L.A. history.

Considered one of the first, if not THE first, houses in Hollywood, it's been dubbed the Original "Outpost" after the founder of the L.A. Times, General Harrison Grey Otis, had it all to himself back in the 1880s.

After its demolition, the current home was erected in its place and changed ownership a few times before finally coming into BB's possession, where he lived for 50 years.

Bob -- who died in August last year at the age of 99 -- didn't make any changes to the property since purchasing it in '69 ... so it had loads of its OG charm and features.