In town, not ever as long as I stay off a couple problem streets like Hulen. I actually live 35 miles northwest of town, and get honked at more on the country roads. I am refering to actual Fort Worth, not the mid-cities area between there and Dallas. I used to leave my car at the lot where I work and do any erronds I needed to run by bicycle before work when I worked nights. I still ride to downtown rather than drive if I can.

Look at the map of the Trinity trail network, you can get anywhere you need to go with only hopping on side streets off the trail.