In the first paper below, they studied how much it takes for a healthy tendon to grow by adapting to stiffness when exercising. It is suggested that tendons change slowly after more than 8 weeks of exercises as long as the loading being put on the tendons exceed 70% of what they can withstand (e.g. 70% of the participant's weight for Achilles tendon). For upper extremities, this can be interpreted as 70% of one's full strength as it it difficult to load them with 70% of your weight.

The second paper states that the 12-week eccentric exercise program (3 sets x 15 repetitions twice a day, more than 6 days a week) was effective in treating the Achilles tendon problem. Therefore, it can be concluded that it takes about eight weeks to change a healthy tendon, and about 12 weeks to change a painful tendon. Although this study was on the Achilles tendon, the rehabilitation of biceps tendon is not much different.

However, the exact duration may vary depending on the individual and the affected area. If your pain does not allow you to exercise the affected/weak tendons with more than 70% of the load, it may take longer. On the other hand, if you effectually reduce the stress on the tendon through an effective exercise program, the pain can disappear within a 4-8 week timeframe. You will have the best chance at shortening the recovery time with this program.

References

Bohm, S., Mersmann, F., & Arampatzis, A. (2015). Human tendon adaptation in response to mechanical loading: a systematic review and meta-analysis of exercise intervention studies on healthy adults. Sports medicine-open, 1(1), 7.

Beyer, R., Kongsgaard, M., Hougs Kjær, B., Øhlenschlæger, T., Kjær, M., & Magnusson, S. P. (2015). Heavy slow resistance versus eccentric training as treatment for Achilles tendinopathy: a randomized controlled trial. The American journal of sports medicine, 43(7), 1704-1711.