In Bridge, Is There A Way To Shorten "Reaction Time" For "Real Time" Play
In tournaments, there is no time limit, official or unofficial for a hand or trick; taking 5 minutes to play to the first trick is not unusual.  Tournaments don't grind to a halt (i) because there is usually a time limit for a section or session (so you play most hands quickly and have time to spare on the tricky ones) and (ii) because by the time somebody has reached tournament level, he or she will have enough experience to recognize the simple situations (draw trumps/crossruff, duck a trick/cash winners), and will only take a long time for genuinely complex decisions.  The only way to reach this point, I am sorry to say, is practice. Find a group who take the game seriously enough to take time over it: join a duplicate club: make a mental note after every hand of the one thing you want to remember about it.  And then get some more practice.  It won't on its own make you a good player (ask any of my partners), but it will improve your speed.

(There is also the factor that tournament players have to write down their system of bidding and discards, so don't have to worry about remembering them; but it sounds like you shouldn't worry about that at present.)