With all questions of this nature, you just need to remember that the best training for a given activity is… doing that activity. So, if you’re looking to get faster over the tri bike leg, at the simplest level, the most effective training will be riding in as close to race set-up as possible.
What’s the difference between a road bike and a mountain bike?
However, in the real world, other factors can impact on adhering to specificity. Do you always want to be riding a race set-up? What about if it’s icy out? For me, I enjoy mountain biking; it improves my bike handling and confidence, etc. So, my advice is, especially in the off-season, as long as you’re cycling you’ll be helping to improve your bike speed and strength.
But as you move into the season, that’s when you need to start thinking about increasing specificity. You should be looking to mimic your racing in your training. With regards to position on the bike, wattage, cadence and the roads you ride on, the closer you match the demands of your target events, the better adapted to them you’ll be on race day.