I would like to play the Effects & Presets animations in Bridge but cannot see the play button

Bridge has always been buggy when it comes to playing back animation presets. Only the animation presets that come bundled with AE have previews. If updating Bridge and After Effects, so they are both on the current version and waiting a very long time for a preview to be generated does not fix the problem you are probably out of luck. It's usually faster just to read the descriptions and double click on the presets you want to try. A quick undo will let you start another one. Any time I use the built-in presets I always modify them anyway. None of them work perfectly for me without a little tweaking.