Connacht had levelled through a Dave McSharry try after falling behind early on, but they simply had no answer to Ulster's dominance - even if Darragh Leader also touched down.
Trimble secured his treble just before the hour mark while Luke Marshall and Craig Gilroy also crossed in a convincing home win.
The game was just four minutes old when Ulster drew first blood with a try in the corner from Paul Marshall, the scrum-half sniping around the side of the breakdown.
Paddy Jackson pushed the difficult conversion wide and things went from bad to worse for the home side as Connacht drew level on seven minutes as McSharry exploited an overlap on the left-hand side.
Dan Parks also sent the tough conversion wide but on 11 minutes Jackson found his range, bisecting the posts after Connacht were penalised for not releasing.
And Ulster extended their lead after quarter of an hour as Trimble went over on the wing, Jackson once again wide with the tricky conversion.
Try number three arrived on 23 minutes, this time Trimble playing the role of provider as he broke before offloading to Bowe - fly-half Jackson this time converting, albeit off the left-hand post.
And just moments later Ulster had wrapped up the bonus point as Paul Marshall grabbed his second try of the game, Trimble once again setting it up.
Jackson once again converted and sent over a penalty just before half-time as well to allow his side to go into the break with a healthy 30-5 lead.
And Ulster didn't let their foot off the pedal in the second half, scoring a fifth try just two minutes after the restart. This time Bowe repaid the favour but setting Trimble away, the winger running from just outside his own 22 before touching down. Jackson converted and Ulster lead 37-5.
It was the Luke Marshall's turn to get in on the act as he finished off a brilliant move involving Jackson and Darren Cave to mark his 50th Ulster cap in style.
Jackson converted and on 57 minutes Connacht were down to 14 men after Michael Swift was shown a yellow card by referee Ian Davies on his 180th appearance for the club, just three minutes after coming off the bench.
And moments later Trimble was celebrating a hat-trick, Michael Heaney setting it up after replacing Paul Marshall, Jackson once again converting.
Replacement winger Leader gave the travelling Connacht fans something to cheer on 62 minutes as he grabbed a try, Miah Nikora converting.
However their joy was short lived as left wing Gilroy grabbed Ulster's eighth score, racing onto a James McKinney kick through to touch down.
McKinney had replaced Jackson but picked up where the Ireland international had left off, sending the conversion through the uprights.
Robbie Henshaw thought he had a late try but he collected Nikora's cross-field kick with one foot out of touch with the visitors delighted to hear the final whistle.
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| Ulster Rugby Score Card | |||||
| Name | Tries | Conv | Pen | Drop | Pts |
|---|---|---|---|---|---|
| Tommy Bowe | 1 | 5 | |||
| Andrew Trimble | 3 | 15 | |||
| Paul Marshall | 2 | 10 | |||
| Luke Marshall | 1 | 5 | |||
| James McKinney | 1 | 2 | |||
| Craig Gilroy | 1 | 5 | |||
| Paddy Jackson | 5 | 2 | 16 | ||
| Total | 8 | 6 | 2 | 58 | |
| Connacht Rugby Score Card | |||||
| Name | Tries | Conv | Pen | Drop | Pts |
|---|---|---|---|---|---|
| Miah Nikora | 1 | 2 | |||
| Dave McSharry | 1 | 5 | |||
| Darragh Leader | 1 | 5 | |||
| Total | 2 | 1 | 12 | ||
| |||||||||||||||||||||||||||||||
