I'm playing with it a bit to see what your problem may be... my pencils have been sadly neglected lately, and I don't work with baby oil very often. I'm going to guess that you have too much oil in your stump, so rather than moving the pigment into the paper, it's floating on the surface. You don't need to saturate your stump, and you may not even need to re-dip it. Are you getting an oil 'halo' at all?
There is a bit of a learning curve to working with baby oil and getting just the right amount, so that will take some practice... you may also want to try a paper with a little more 'tooth' or rougher surface, like the Georgia Pacific cardstock that you can get at Walmart.