Park took the lead after just two minutes through inside centre Matt Gordon's score, converted by full back Joe Luca Smith.
Moments later, winger James Cordy Redden dotted down after two new signings combined for a lovely score as a delicate chip from outside half Steffan James was dotted down at the back of the dead ball area by Cordy-Redden.
Smith made it three tries inside the opening 11 minutes for the third-tier side.
Last season's National Two East runners up, Barnes looked like they were back in the contest when Joe Henry scored the first of his two tries, this one converted by Angus Graham, however it remained one way traffic for the remainder of the first half.
A beautifully worked set-piece move, straight off the training ground, sent Charlie Walker sailing through a gap in the defensive line before the winger executed a simple draw-and-give to put Joe Smith away for his second try of the day. While, Cordy-Reeden added his second to make it 31-7 at the interval.
Hugo Ellis continued the scoring four minutes into the second half and Benji Marfo profited from a helpless defence.
Barnes scored a consolation try on the hour mark through Henry's second score, but Park had the final word when Matt Woodward concluded an emphatic rout. An electric passage late in the game following a scrum on halfway saw Park string together a succession of offloads to drive the visitors back towards their own line before a well run hard line by Woodward sent the tighthead in under the posts.
Bournville completed their match preparations for the new National Two West season with an emphatic victory at Dore Moor.
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