The Hammers are a point from safety and travel to Manchester City on Wednesday before visiting Liverpool on Monday.
Bowen made a £22million deadline-day move to east London and Moyes is hopeful he can add the pace and goal threat they have so desperately lacked, but is wary of throwing him in at the deep end.
"I have been pleased with what I have seen from Jarrod at the moment," said Moyes. "He’s come in and settled in very quickly, he’s looked very sharp in training.
"He’s obviously had loads of games, it’s not as if he’s short of match practice or match fitness in any way so I have been pleased. But I am also wary of putting the boys in too quickly. I have had lots of boys from the Championship in the past and I think it’s important that you put them in at the right time, the right moments, at the right time and we will just take our time and see when it’s right for Jarrod.
"Obviously he is a talent. We need goals, he can do that. I am also very aware that we don’t need to put pressure on him too quickly."