I am a recently retired urologist, practiced for 37 years, cyclist since about 1988. averaged 6-8000 miles per year, . I can tell you it is much more likely urinary issues after cycling are coming from your urethra(the tube the urine flows through)rather than your prostate, unless you have a very large prostate ( which btw most doctors have no clue about prostate size) urethral pressure and cause voiding symptoms. Anatomically when you are sitting on the saddle and leaning forward on your bars, your prostate is away from the saddle unless you have an extremely upright position. Coffee or energy drinks with caffeine will increase your urine output and increase bladder sensitivity and make you go more often.
Tamsulosin is a great medicine, dutasteride not so much, and saw palmetto and all OTC meds absolutely no proof they work. Now saying there is no proof that they work is not the same as saying there is proof they do not. They won't hurt you so take em if you think they work. You might get some help from a urologist but unless your urologist cycles good luck. If you are taking saw palmetto or dutasteride(aka Avodart) or finasteride(aka Proscar) be sure and tell the urologist as all can give a false low reading if they measure your PSA-prostatie specific antigen, cancer screening test.