Both of the bathroom toilets let out an air bubble when flushed and the water sometimes splashes outside the rim. I air bubble is rather large. But they do flush.

Clogged vent line or partial downstream blockage. As the water flows down, the line can't vent and the air is venting back through the toilet.

This indicates a partial blockage. You have several options.
1- You can pull the toilet and snake from there **or**
2- Snake from the lavatory roof vent. Put out enough snake to reach the base and 15 more feet. Good luck, Tom