Question about Staining & Finishing Turned Ash

Hello,
New to LB and trying this out to help solve a problem. I have a project that is made from turned Ash, and have had a difficult time staining the wood. My process has been sanding to 220 then using a Lockwood water based stain applied thin in a couple coats. I achieved the color I want for the most part, some parts are a bit darker than others due to grain changes as the piece is large and made from glued up parts. I then applied Watco Danish Oil- natural. On the second coat I very lightly wet sanded with 320, and when wiping off the excess oil noticed a dirty rag as some of the stain must have come off from wet-sanding. On the third coat I wet sanded with 600 hoping to avoid removing any more stain, but even with the lightest touch I went through in a couple small spots and reveled the light color wood. Also, it seems like the areas without much grain activity have lightened up. Seems obvious, but I have to say I barely touched the wood with the paper. I feel like the stain is not being absorbed into the wood, and is resting on the surface- contrary to what I believed a water based stain would do.
Any suggestions?