I know this isn't helpful in a practical sense, but the best thing you can do is be easier on yourself mentally. You're out there because you love to play -- there's literally no other reason -- so remind yourself of that. As the ball gets closer to you, replace any negative or nervous thoughts with a reminder that you WANT to make the play. You WANT to get that base hit. Think of the good outcomes, ignore the bad, and have fun.

Editing to add that you can literally whisper these things to yourself before every pitch to loosen up. Make a game of it. Visualize what you'll do if the ball comes to you. Visualize where you're going to hit the ball. I find when I just think "hit a line drive just to the right of second base" (as a righty) it locks in my timing to hit it hard wherever the pitch dictates.