The more lube you put in the bearing the more responsive it will be. What you should have for inresponsive play is a very lightly oiled bearing, just enough to protect it from moisture and decrease the noise but not enough to add response. As mentioned by sniffy and throwrw, you should give it a cleaning either in acetone or something that works as a good degreasing agent and let it dry.
Don’t be afraid to try other oils in the bearing also. I have several made for yoyos but also some brands I’ve picked up from the local hobby store that are very thin and work well. Best way I’ve found to apply lube to maintain unresponsive play is exactly like throwrw suggested, don’t drop the lube in right from the bottle but use a pin or toothpick to apply it little by little. Remember that you have to take the shields off to do this and apply the lube to just a few of the balls in the bearing. If you add a bit too much don’t run to start over but just play the yoyo and it will break in and be just fine. Of course if you add to much though and find that your spin time is awful or the yoyo is responsive clean the bearing and start over.
What I’ve done in the past is to clean my bearing, put it in the yoyo and give it a throw. I see roughly how long it will spin with a dry bearing and I try to get the same time out of it after I lube it. This gives a good basis for comparison so you know if you have added too much lube.
And don’t be afraid to try out different amounts of lube, the bearing isn’t as delicate as you think.
Good luck and come back if you have any more questions.