Westwood started the previous two matches - wins over Preston and Middlesbrough - but was surprisingly not in the matchday squad for the draw at Albion.
Cameron Dawson replaced Westwood in goal and Bullen said afterwards that the Republic of Ireland stopper was left out as a precaution and that he is likely to return between the sticks for the Birmingham game on New Year's Day.
"There's no real issue," Bullen said.
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"He's not injured. It was two games in 12 months that he's played.
"He's 34-years-old and there's a few aches and pains but certainly no injury.
"It was one that we discussed.Â
"If he'd played (today) he could have got injured.
"It was a similar issue with Steven Fletcher.
"Westy had been out for so long with an injury so the last thing we wanted is a long-term injury again.
"On the balance of play it was probably the right decision.
"He will be fit and available for selection come the Birmingham game."
West Brom levelled in stoppage time when former Owl Chris Brunt tapped in from a corner, with the final touch being given as a David Jones own goal.
Bullen said it was a bitter pill to swallow, especially for Dawson.
"I was devastated for Cammy because he knows how well he played," added Bullen.
"For all the possession they had and the pressure they put on us, I can't remember him having to make a worldie save.
"He had a fantastic performance but is sitting inthat changing room without a clean sheet.
"We had to call on him today and he was outstanding."