Full Idea
The view that time has a direction is entirely consistent with the B-theory of time, as long as time's having a direction is not a matter of it having temporal flow.
Gist of Idea
The B-series can have a direction, as long as it does not arise from temporal flow
Source
Baron,S/Miller,K (Intro to the Philosophy of Time [2019], 5.5)
Book Reference
Baron,S/Miller,K: 'Introduction to the Philosophy of Time' [Polity 2019], p.136
A Reaction
I'm not sure how you could account for an intrinsic direction to time if it is not because of the 'flow'. The B-series seems to invite a reductive account of time's direction (e.g. to entropy).