Is it better to learn to play bridge by reading about it, or just playing?
I think you'd be hard-pushed to learn Bridge just by reading about it.  There are many, many excellent books out there, but until you're sitting down at an actual table it will be hard to visualise what it actually feels like, having only partial information, trying urgently to communicate your hand to your partner despite your opponent continually getting in your way.

Equally, I think it'd be a slow process learning Bridge just by playing it.  Sure, you'll get better and better as the fundamental concepts begin to dawn on you; but Bridge is an immensely subtle and sophisticated game and some of the finest game-playing minds of this and last century have thought about it for millions of hours.  Reading some of the greatest writers on the subject will be a short-cut to ideas and epiphanies that would take you years or decades to stumble across in the course of playing with just the basics under your belt.

So to answer your question, yes I would "just master the most basic rules and then try playing"; but I'd make sure to keep reading more, then playing more, then reading more again!  Bridge is an incredibly deep game, perhaps unequalled in depth by any other game - you could easily spend your life playing it, mastering it, assimilating the ideas of others who have tried to master it.  It's well worth it though - I envy you your journey!