Does it need a new bathroom because you don't like the look of grey, is it still functioning? If it all still works then I'd just live with it - save up and do a proper job the first time with a shower etc.
I did it in my kitchen and on my fireplace. Tried Dulux first, which was crap so scraped it all off and used Ronseal. Even my picky DM thought they were new tiles. I put the paint on with a gloss roller (much easier than a brush and no brush strokes visible) and then went over the grout with a white grout pen. Saved me loads of time and effort.
I have lived with worse for 5 years but to get what you want in the end is worth it. We replaced the carpet with the cheapest lino we could find - would have painted but is was all tiled - after a little while you will stop noticing how awful it is.