I went through something like that in 2006. I started riding because of my BF at the time who was a cyclist. Admittedly, it was tough to disassociate the two, and to be honest, I didn't really do a great job of it in that I continued to more or less ride with the same group of people--including him--that he introduced me to. In some ways, that worked for me because those people were and remain wonderful friends and cycling buddies. In other ways, it prevented me from moving on as quickly and cleanly as I might have otherwise. It was, at best, a calculated risk.
My advice in this: Regardless of whether you continue to ride, the breakup is going to hurt and you're likely going to be thinking of him regardless. Accept that. So, wouldn't you rather hurt while you otherwise did something that you enjoyed and was good for you? Find ways to ride that don't literally and figuratively cover the same ground that you covered with your BF. Identify different cycling goals, different routes, different people with whom to ride. In time, you will associate your bike less and less with him.
Ask yourself this: In a year's time (give or take), do you want to be the woman who found a way through her pain to continue to do something that she enjoyed and that was good for her body, mind and spirit or do you want to be someone who abandoned herself and one of her favorite hobbies because it otherwise hurt?
I don't put it in those terms to sound unkind. Trust me when I say that I've had heartbreak, too. It's awful, and I'm not trying to minimize it. But at the end of the day, how do you want to define yourself? By your breakups or by your own terms? If it's the latter, then you will find a way to continue to love your bike, cycling and competing in tris. It will not be easy, but it is doable. Plus, on the other side of the pain, is a renewed sense of your own power and strength.
I'm still friends with my ex. I'm also married now to someone else that I met through cycling. In between those relationships, I made good friends, traveled and found a person within myself that was far better for having continued to ride. It all worked out for the best.
Hugs and good luck.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher