What are the distances for your (mini)-Tri? Is it a 'road' Tri? There are different length "traditional" road Tri's.
For shorter distance events, a good endurance base is helpful - and is all that is really needed - to *finish*. Finishing your first Tri is all about adjusting to the rigors of transitioning from one 'stage' to another. Having that endurance base and focusing on completing each of the 3 legs of the race at a 'comfortable' pace is key.
As mentioned, there is no shortcut to endurance events like Tri's. You can't expect to do well/finish if all you're doing are short intervals. But you can mitigate some of that by making your 'interval' workouts more intense (harder efforts) and/or combining 2 or more of the elements of the Tri in your workouts. One of the more common workouts for multi-sport athletes are 'brick' workouts - you combine a ride and run (B & R, hence 'brick') in one workout. This helps your body acclimate to the switch from biking to running. It can also be done with a swim, but the logistics are a little more cumbersome. But the basic idea is to combine the elements of the Tri in one workout to give your body the chance to adjust to the rigors of the different elements of the Tri.
For a shorter Tri though, you really do not need to do really long workouts. A decent 5-10 mile bike ride combined with a 2-3 mile run IMO is a good start. If you're in as decent a shape as you say, this shouldn't take but an hour or so. I'm not much of a swimmer so I can't give you a good reference for that. I do mostly Duathlons (run-bike-run) for now - but I am working on getting some swim training in. In reality though, you really need to schedule at least 1 'long' workout day in your week to fully prepare for an endurance event like a Tri. That's really the best way to acclimate your body to the rigors of an endurance event.
Now whether you're going to try and place or go fast ... that's another story.
Sprint Tri: 800m (~1/2mi) swim, 20k (~12mi) bike, 5k (3.1mi) run
Olympic: Tri: 1500m (~1mi) swim, 40k (~26mi) bike, 10k (6.2)run
Half Ironman (HIM): 1.2mi swim, 56mi bike, half-marathon (13.1mi) run
Full Ironman (IM): 2.4mi swim, 112mi bike, full-marathon (26.2mi) run