Generally speaking, triathletes lack bike handling skills when riding with a group of cyclists for one of few reasons: they don't race bike races, triathlon courses consist of very few turns, and unless they're racing ITU races that are draft-legal, drafting is not allowed in triathlons. "Athletes must keep a distance of 7 meters (~4 bike lengths) between bikes except when passing. Failure to do so will result in a drafting violation." Cyclists however, have to deal with technical turns, jumps, accelerations; riding in and around masses of people. They have to be quick on their feet, and there's no "zoning" out in races unless they're doing a time trial as part of a stage race, for example. But, bike handling skills can be improved by riding/training with cyclists more often. Mix it up, cyclists are cool people to be around…once you've earned their respect. Warning: there are cyclists out there that have terrible bike handling skills. Work towards hanging with the elite/experienced riders, but find the right ones and don't be stubborn--learn from them. Lacking bike handling skills go hand in hand with little group riding experience.
The bike leg of a triathlon is more of a steady pace when comparing it to the speed inconsistencies of a criterium or road race, let's say. A triathlete might be able to average 24-26 mph in a triathlon for an entire 56 miles, but the same can be true in a 25-30mi criterium. However, in a bike race, accelerations and decelerations are so prevalent, you just can't compare the two. Since triathletes aren't allowed to draft in triathlons, their mentality is to train on the bike with a racing mentality. For example, one might think, why draft off of each other in a training ride when you aren't allowed to do it in a race? But, every now and then, they may hop in a predominantly cyclist group ride, and this is where the "problems" arise. Not that they're trying to be assh*les, they just don't have the experience or awareness of respecting the etiquette of a group ride. I know when I started riding with cyclists, the concept of a paceline was new to me. I was apprehensive, but I watched, I listened, I learned, and I have matured. It has made me into a stronger rider.
Like for any triathlete, there are also hard days and there are easy days for cyclists. Pick and choose the right training rides. If you want a hard training session aside from a TT-specific workout, go for the Derby or the Thursday Night training crit races (aka Thursday Night Worlds), both starting or located near our very own Cycling Center. Local triathletes aside from me will probably never do the training crits whether it be because they aren't comfortable being in such close proximity with other riders, they're afraid of crashing, it requires a USAC license, but mostly because they don't do bike races. Which is totally fine and understandable, but it's the secret weapon to my triathlon training. Very rarely does my bike training fail on me during triathlon races…hoping it pulls through in two weeks.