Will my bike times be faster in a race

Yea generally faster, adreniline makes you go faster. Plus you should be a bit more rested.

In general, most people put up faster times in a race... for me, I think every race I have done has ended up being faster than the bulk of the training I did for the race.  Same goes for the run.

Doesn't necessarily mean yours *will*, but usually that's the pattern I've seen with people around here.

You will probably be faster in a race. For one thing, it's rare that you're able to go out for a training ride without ever having to slow or stop for traffic, other riders/pedestrians, etc., and all of those things will affect your overall avg. speed for a ride. Of course, your pace during a race will vary depending on factors such as weather conditions, wind, and flat vs. hilly course.

Hard to say as race course and terrain effect speed a lot. I can ride one race course 20 mph and another 17 and the difference is terrain.

Other thing is you did a 10 mile run yesterday and when is your race? What's the distance of your race? Coming into the race fatigued is not good. Not sure how running 10.2 miles yesterday will help your legs be fresher for the race.