Roman regiments of the VIth century.

[Robert Vermaat]

Both. They're graded as Auxilia Palatina but served as Bucellarii.
Bucellarii was a role, not a unit type.

Which means they can very well have originated as a unit of Gothic bodyguards to Galla Placidia, before entering the ranks as a regular unit. We are of course talking mid-5th century here, and distinctions between irregular units and regular units could be very vague even during the Principate. Plus if we recall the savage Atacotti, who may have entered into a regular Late Roman unit, the guard of Galla Placidia will have been much closer to a regular unit.

My guess is they became 'official' after the had to be paid for by the Roman treasury.