The hosts very nearly doubled their advantage following the interval, Mowatt’s curling effort striking the post and bouncing clear.
Instead, Portsmouth equalised on 56-minutes. Josh Murphy whipped in a cross, which Bishop made no mistake in flicking home.
A strong Albion penalty shout was turned away after Heggebø looked to have been brought down inside the box – and the referee sent Head Coach Ryan Mason off shortly after.
Despite a lengthy stoppage time, the Baggies couldn’t find a winner, having to continue their unbeaten start to the season with a draw.
Albion: Griffiths, Furlong, Phillips, Campbell, Styles, Fellows (Wallace 87), Molumby (Collyer 87), Mowatt, Johnston (Grant 60), Price (Maja 82), Heggebø.
Substitutes: Wildsmith, Taylor, Williams, Diakite, Cole.
Attendance: 24,818 (2,473).