Have you taken the MSF?
Here are some tips from personal experience.
-Look where you want to end up going, in this case look 90 degrees to the right
-Lean the bike by countersteering, but keep your arms as loose as possible on the bars. Let the bike turn itself, don't fight it. This applies 100% of the time when riding. Do not death grip the bars, especially in turns.
-Once you are in the turn, get back on the throttle and slowly roll it on as you exit.
-Most importantly, trust in your tires. They will not slip so long as you are not going insanely fast or hit a slippery surface.
It just takes practice...I know the feeling you are referring to when you say the bike feels like it is going to slip. It's ALL in your head, that you must understand to become a better rider.
Safe cornering
