While criteriums (also called “crits”) and road races are super training for triathletes, they do involve a bit more risk, specific bike-handling skills, and (very) close group riding experience. If that is a concern, search for a time trial or hill climb instead and feel confident that you’ll fit in just fine. (Note: Your tri bike will work great for any TT, but you may need a bike without any aerobars for a hill climb, especially if it is a mass-start event.)
In addition to easy-moderate riding, include a weekly session of 3×10 minutes at threshold (the effort you could sustain for one hour continuously when highly motivated). Take a five-minute easy spin between each hard effort.
While the first rule of any time-trial event is “don’t miss your start time,” a very close second is “don’t go out too fast.” For help with the second rule, rely on data gleaned from your most recent 3×10 workout to provide you an objective effort “ceiling” not to be exceeded in the first five minutes. Your average effort, HR or power for this distance (usually 40K or less) will then represent your very best of the early season given you should be saving nothing for the run.