Bower, who recently won the prestigious Brabazon Trophy, shot a two-under-par 69 to lie two shots behind first-round leaders Kristoofer Ventura, of Denmark, and Finland's Kim Koivu.
He dropped a shot at the third, but made rapid amends by birdieing five and six.
The Yorkshire champion was back to one over par after successive bogeys at seven and eight, but followed with three birdies in four holes from the ninth.
The Gauteng North Open and Southern Cape Open champion shed the fourth shot of his round at the 13th, but closed with a birdie at the last.
England's other players saw Bradley Moore also card 69, new Amateur champion Scott Gregory a 72 and Lytham Trophy winner Alfie Plant a 73 while Marco Penge totalled 77 and Adam Chapman 78.