Perfect your technique. To really feel when you play trumpet, you need to be thinking about the music and not the notes. Practice slowly, so you have time to improvise innovative things instead of what your hands know best. Practice scales and technical exercises, too. These will help your playing immensely. If you are a serious trumpet player, it's best if you block out an hour or two of your daily practice time just for technique.
Relax. There's a reason music teachers are always telling their students to relax --- it makes a difference. Ideally, you'll feel the same in front of an audience as you do in the practice room. Tell yourself that there are no wrong notes. Sure, there are notes that don't go with the music, and there are notes that aren't written on the page, but that didn't stop great artists like Miles Davis from playing them anyway. Try meditating, or come up with a pre-performance relaxation routine. This will help the music flow through you more easily.
Practice performing. If your mind isn't used to being onstage, you're going to clam up when you do get in front of an audience. Put aside a segment of your practice time to practice performing. Visualize being backstage. Then walk out onto the "stage" and take an imaginary bow. Visualize the audience in front of you as you go through your repertoire.
Listen to lots of music. If you want to feel the music when you play, then you probably already love music. Surround yourself with music whenever you can, especially the type of music you like to play. Think about the private meaning music has for you, and think about meaning when you're playing your trumpet. When you get to a point where nothing matters but the music -- not the audience, or your teacher, or the money you might be making, but the music -- you'll be well on your way to really feeling.