So im new too this game, and i found lava should i be worried that i might run into a lava pit from the side and have to indian jones run out of my mine shaft? or is there bedrock or something preventing me from mining lava from the side?
Lava isn't 'spawned from bedrock'. It can come out of any rock. You might even find it in pools on the surface, or flowing out of a mountain side.
It doesn't flow as fast or as far as water (it only flows 'out' 3 blocks from the source block). If you dig into a lava lake from the side you should have the time to run a few blocks away. You should also be able to stand back and plug the hole. Dig up and find the surface of it. Go from there.
Just follow the Basic Rules Of Minecraft and you'll be ok: Never dig straight down (never dig the block you're standing on). You might fall into a lava lake. Never dig straight up. You might punch through the bottom of a lava lake, or just about as bad, punch through and gravel or sand fall on you and kill you.