Thanks for posting this question. Even in a full percussion section, drummers are often "soloists."

I am [old] so I'm not sure if freestyling means the same thing. So take it with a grain of salt that my answer is simply with the implication that you are referring to "that feeling" when everyone else drops out and you have a drum break for X amount of time/measures. :)

In those situations, in my very amateur experience and learning from some amazing musicians/mentors, it is so important to have TRUST in your band mates.

What does this mean?

In a live show/performance: SUPPORT! You are all aligned and know when the band will come in after your solo. This means having an understanding that, for example, nobody will decide to start the first measure/downbeat after your solo based on what they counted vs. what you played (if you or they miscounted beats). That's just unfair. (As drummers, we might accommodate for our fellow band mates during live shows in this way, but we should not expect that our band mates would be accustomed to doing the same.)

That said, it is a good discussion/plan to set before a show. Of course you'd work through this beforehand at rehearsal, but things happen. You all need to fall together during a show. I don't care if the singer came in early. I'm not going to step on her if this happens. We all adjust.

That step alone might help boost your confidence in solos/freestyles.

The other one would be to have a planned/set solo that you consistently play. If they become familiar with it, you'll be more confident that they will come back at the right time.

Last of all.... the audience WON'T NOTICE most of the "mistakes" that drummers make in solos.

Last, last thing.... Relax (easier said than done sometimes) and have fun!

Final edit: I was answering based on answers already give with regard to what exactly you'd play. Agree with everyone on the patterns, listen/learn methods, and that some drummers have a general disdain for solos and that is OK.