Not doing any heavy lifting for work or other?
Note that static stretching just prior to tennis or other exercise is not usually the best idea. Do those types of stretches after tennis or 30-60 minutes or more prior to tennis. Dynamic stretching and warming up are a much better idea just prior to tennis. As part of your warmup, perform some shadow swings. This should include some shadow serves to warm up your arm, shoulder and core. Arm & fingers should be fairly relaxed when doing this -- do not tense up any more than absolutely necessary.
I don't believe that biceps injuries all that common -- certainly not as common as other injuries of the arm such as TE, GE, wrist or shoulder/rotator problems. Note that the triceps are used more forcefully for a tennis overhead than are the biceps. The biceps are used for for bending the elbow and for supination (when the elbow is bent).
Can only speculate what might be happening with you biceps tendon. Are you trying to "muscle" your serves? You might be tensing the biceps and other muscles too much in an attempt to hard serves (or more kick). Keep the arm as relaxed as possible. You should be able to generate power or racket head speed with your fingers and arm fairly relaxed -- just let them tighten up naturally on their own.
I wonder if you might be rushing thru the trophy phase of your serve. Some ppl move thru this phase much too quickly to get to the racket drop (scratch position). Note that there should not be a pause at the racket drop while waiting for the ball toss. If you have a pause at that point, you may be rushing thru the trophy phase.
Are your biceps naturally tight? If they are, and you are hyperextending your arm on your serve, you might be stressing the distal biceps tendon. Your arm/elbow should be comfortably straight at contact (not hyperextended).
Any unusual or forced/explosive supination in your service motion?
Poly strings? Is your racket arm-UNfriendly?
