If you loosen the strings, that saddle bar probably comes out and you could sand the bottom of it to get the action you want.
However...
I'd take all the strings off except the A string, since that's what's readily causing the buzz and try to isolate the source of the buzzing first. Hit the string, make it buzz, then put your fingers on what you suspect is vibrating and causing the buzz. Apply pressure to stop the different bits vibrating, e.g. the saddle, the ball ens of the string, the ends of the bridge against the body, check the truss rod isn't slack, strap buttons, tuner keys, even the bracing inside the sound hole.