The five-time world champion began his title defence in style, posting breaks of 88 and 90 to lead the Irish amateur.
In the third frame, O’Sullivan was building towards a rapid maximum, but chose to go for the pink after the final red.
O’Sullivan could be heard saying ‘It’s alright!’ to the crowd after there were some audible groans.
He went on to post 133, as though he potted a difficult blue on the top cushion, he missed the subsequent pink.
O’Sullivan was clearly in no mood to hang around in York, hitting the yellow in the next frame before the referee had replaced the brown.
A foul was called, but the break of 66 was enough to hand O’Sullivan the fourth frame as Bulman watched on.
O’Sullivan closed out the match after winning a tight fifth frame before wrapping it up with a 65 in the sixth.
Elsehwere, Shaun Murphy became the biggest casualty to fall in the opening round of the UK Championship after losing 6-4 to world No 125 Eden Sharav.
Murphy, ranked eighth, led 3-1 in York, but the 2005 world champion was then stunned as Sharav won five of the next six frames.
Breaks of 70 and 62 moved the Israeli-Scottish Sharav within a frame of victory, and he held his nerve in the 10th after it went down to the final black.
Mark Allen advanced after breaks of 64, 129 and 56 help the world No 7 see off Jimmy White 6-3.
It was a valiant effort from White, who took a 3-2 lead, but Allen won four on the spin to seal his spot in the next round.