Fellow wing Andrew Trimble and full-back Jared Payne also crossed the whitewash while hooker Rory Best grabbed the other and Ruan Pienaar kicked nine points.
Connacht gave as good as they got for much of the game but first-half tries from George Naoupu and Fetu'u Vainikolo ultimately proved too little to stop Ulster cementing their place at the top of the table.
Ulster began the game in disastrous fashion, knocking the ball on from the kick-off and then being penalised in the scrum.
Pienaar was then tackled inside his own half and once the ball was stolen it was thrown wide to Naoupu who went over for the first try.
Pienaar missed the chance to reduce the gap to two points when he failed with a penalty attempt in a swirling wind but it wasn't long before the league leaders were in front thanks to a fine try.
Darren Cave was at the heart of a flowing passing move that also featured Payne before centre Olding timed his run perfectly to collect the ball and fly over the whitewash.
If that was good then Pienaar's assist for the next try two minutes later was superb. The South African cut in off the left wing before flicking the ball out the back of his hand for the motoring Trimble who was never going to be stopped.
Pienaar missed the conversion and Ulster's seven point advantage was wiped out on 17 minutes when Eoin Griffin and Gavin Duffy combined to release Tongan wing Vainikolo who beat three men to score the try and Dan Parks added the extras.
Parks and Pienaar then exchanged penalties before Best finished off a strong maul and Pienaar converted to put Ulster 22-15 up at the break.
The gap was reduced to four nine minutes after the teams reappeared when Miah Nikora slotted a penalty from in front of the posts after Connacht had failed with a drop goal before play was brought back for an infringement.
Ulster almost found the breathing space they were looking for when Payne crossed the try line only for him to he held up in the tackle.
The visitors continued to pile on the pressure from the scrum but despite a series of penalties Connacht managed to stand firm.
However, the hosts were powerless to prevent Ulster sealing the bonus point when replacement lock Iain Henderson embarked on a bulldozing run and fed Bowe who finished off the move.
Pienaar convered to make it 29-18 to Ulster and there was more to come when Payne ran in from almost half-way to cross in the corner.
|Connacht Rugby Score Card|
|Ulster Rugby Score Card|