Time Trial / Time Trialling / TT

Is there a relatively easy way to search CTT events that have a separate road bike category?

No. Most events which have multiple category classifications are all bundled up into one event. You need to obtain the prospectus from the event secretary, which will list all the prizes on offer. This is obviously a massive PITA since very few of them pro-actively publish anything like a prospectus. When you have been doing TTs for 30 years or so, you'll have gained a fair knowledge of which event secretaries are even worth asking about such things :)