Bardock being 10,000 was given in the special, right? But the comparison of him and King Vegeta wasn't made in the original Japanese special, right? I remember that when I watched it with Brazilian dubs (which are a lot more faithful than Funimation's, a lot more), one of the workers, doctors from the tub recovery, said he was getting close to King Vegeta, though I was later pointed out it wasn't said as such in the original, there wasn't such line.
However, King Vegeta > Bardock should still stand, right? One would believe if he surpassed or equaled the king, someone would say it.
So a 12,000 battle power seems appropriate for the King, right? With Vegeta surpassing him not being implied in the special and as Kenshi said, could be later on, like when Vegeta was 14, 15 years old.
Though would Bardock be stronger than kid Vegeta or would that be pushing it, i.e, the same would be stated? If it didn't warrant a statement, then who knows, kid Vegeta could be like 8,000?
Kid Vegeta 8,000
Bardock 10,000
King Vegeta 12,000
Vegeta as a brat (~14 years old) 12,750
Though if Bardock weren't given a power level, I wouldn't have king Vegeta this strong personally. Going solely with the manga, I'd imagine he'd be stronger than Nappa (and thus, 8,000 Goku) but that's it.
King Vegeta : 10,000
Kid Vegeta : 7,500
Vegeta (as a brat) : 10,600
Vegeta : 18,000
It gives more spacing for gains.