OK here is what I have done, the vent pipe runs into the attic... I shot some compressed air down it and made the toilet bubble and blew some junk out the shower drain, I snaked the toilet with a closet snake, I snaked as far as I could with a hand snake that's probably 15 feet with the toilet off, replaced the toilet with new wax ring and the toilet bowl fills then goes down real slow not enough to take solids down, so I had enough and bought a new toilet the titan 4 which says it will flush a bucket of golf balls in a single flush, it worked fine for a week solids and all and now I get the big air bubble and drains real slow, probably could take some solid down but not going to try please help!! This is my basement toilet the main floor works fine and no other drains burp

This "burp" and bubble of yours is sewer gas blowing back from a partial blockage. When you flush a upstairs toilet does the basement one burp? Ant back up from the basement floor drain? I would pull the basement toilet and snake it with a sewer machine and not a wimpy hand held one, Good luck, Tom

Had a plumber come pulled the basement toilet ran 56 feet of 2 inch snake came back with lots of roots, toilet works again but still getting a air bubble, the main drain was blocked and thank God for back up protection on floor drains I would have been knee deep in... lol it's a 6 inch line maybe still a partial blockage? When the busted through the roots I watched the floor drain go from full to dry in no time

Sure sounds like you still nave some blocking that's causing a blow back and a bubble. My bet's on roots at the city raiser located at your curb. If you wish to control roots RootX or Robics Foaming Root Killer that contain Dichlobrnic are two products you could try.
A less expensive way would be to call around to garden supply stores and ask for fine grain Copper Sulphate. Put a 1/2 pound in your toilet and flush it down. Repeat in 6 months.
Hope this helps and thank you for rating my answer, Tom