Can't get my new masonry bit to go further than about 3/4"
You most probably hit a bit of hard stone aggregate in the masonry and you’re using a regular drill and not a hammer drill. 

Masonry bits have hardened tips but on hard stone, the tip will just skip and slide if you’re using a regular drill. 

A hammer drill adds percussive hammering to the drill so that the hardened tip can break up any aggregate or stones in its way. Hammer drills have gotten quite cheap ($30-$50 for a chinesium corded one) so you should think of buying one. 



A rotary hammer which a commenter suggested is a hammer drill on steroids. Bigger, heavier, stronger, and more expensive. Definitely overkill for your purposes but great to have if you’re drilling through hardened concrete, want to make larger or deeper holes, need the chiseling function and so forth.