Must say the originals are pretty crap. Have the same bush and setup on my Genesis Grapil (very similar bikes to be fair, with same parent company). I now replace the bushes every month or so as a matter of course and use a slightly wider bush to increase the supported area. It may not be quite as plush (though with my weight on the linkage I can’t notice any difference), but the wider bushes can be had for less than a £1 each. I ussually order up 12 at a time from here…
https://www.bearingboys.co.uk/product.cgi?action=view&id=17001
Best check they ARE the same size as yours but I would be fairly confident they are (or if not you should find some to fit on that site).
In answer to your initial question, these bushings are happy to run dry or greased. I now grease mine. I I was mianly riding somewhere dry I wouldn’t bother but I would rather grease in there keeping the water out than water and grit!
