It was a derby day to forget for Albion as Aston Villa recorded a 3-1 win in the Premier League Cup Group E opener.
Within two minutes the Baggies were in front when Aram Soleman's low cross was turned in cleverly by Bradley.
That lead could have been doubled on 20 minutes when a long throw saw the ball bounce to Kyle Jameson, but his shot went over.
Villa did have first half chances to equalise, notably when Corey Blackett-Taylor's shot was deflected just wide and Kelsey Mooney couldn't convert a header, but Albion went into the break ahead.
However, Easah Suliman pulled the home side level on 66 minutes as he volleyed home after a good corner into the box.
Five minutes later Jordan Lyden put Villa ahead with a curling free-kick into the top corner.
And the scoring was complete with 10 minutes to go when Harry McKirdy side-footed past Brad House.
Late into the game Albion were reduced to 10 men as Rayhaan Tulloch was shown a red card for a bad challenge.
ALBION: House, Meredith, Ferguson, Jameson (McCourt 76), Melbourne; Soleman, Brown (Clayton-Phillips 88), Chambers (Azaz 76), Bradley, Tulloch; Morton.