The summer capture from Exeter marked last week's 3-2 victory at neighbours AFC Telford United with a well-taken penalty and close-range finish to earn Steve Cotterill's men the win.
Experienced frontman Bowman, 29, is focused on preparing for his first season in League One after notching 27 League Two goals in the last two seasons for Exeter.
And Bowman admits getting off the mark in Town colours early on was important regardless of the fixture being a friendly against National League North opposition.
He said: "If you go into friendlies and you don't score, you are then starting to think 'ah come on, get the first goal.'
"But it was my first game the other night and to get a couple of goals means the shackles are off a little bit, the pressure's off a little bit because I've got my first goal and hopefully I'll carry that on into the rest of the games and the season.
"It was the first time I played more than 45 or 60 in a first pre-season game but legs feel fine, really good. We've worked really hard."
Bowman coolly converted a first-half penalty to bring Town level against the Bucks last week before sliding it to finish Nathanael Ogbeta's fine cross after the break.
Stepping up from 12 yards was not an entirely familiar experience for the former Darlington, York and Torquay man.
But, with regular taker Ollie Norburn away on international duty, the striker revealed he jumped at the chance to step in from the spot when asked by the manager.
Bowman added: "Nerves were kicking in a little bit with the penalty but the manager spoke to me before the game and asked if I wanted to take a penalty if we got one and I said 'absolutely'.
"Last season at my previous club I didn't get the chance to take penalties, there was a designated taker and I was always second or third.
"So I haven't had a penalty for a couple of years now but luckily I slotted it away."
The striker continued: "Before I signed here the manager said he wants wingers who can cross the ball and that's straight away brings joy to me because I want the ball in the box to attack. He (Ogbeta) put in a brilliant ball."