Personally, I'd grab some Timbermate grain filler from Bunnings for the ash body. There's a bit of sanding required, but it will do what you want it to do. I've only used the ebony filler, but if you're planning a natural look, you might want something other.

I'm only working in my first veneer top at the moment, and I won't be using grain filler for that, as it's too thin to handle much sanding.

Edit: I posted this not seeing Sonic's response. He has more experience in these matters