Bunbury, who scored for the reserves in their 3-1 defeat by Wigan in a practice game last week, has enjoyed a brief trial spell at Stoke after jetting over from Kansas City.
"He's done smashing, mixed in well and got a goal the other day," Pulis acknowledged.
"Whether he's what we want for the next step, we'll have to see.
"But he's a nice kid and, like most American sports people, is very dedicated. His attitude during his time here has been first-class."