A "herd of cattle" is perfectly acceptable where I come from. Unless there was some doubt about what kind of animal it was, however, you would usually just refer to the "herd". A "herd of cows" is also acceptable if that is, indeed, what they are.
And I dunno what kind of Herefords Bill made the acquaintance of, but a Hereford bull is just as likely to have a go at you as any other I've encountered although Jersey bulls are reputed to be downright deadly.
Here's a funny story, quite true: Years ago I was tramping (read "hiking" you blithering heathens in the US) up the Matukituki Valley near Wanaka. The first part of the tramp is over the top paddocks of Mt Aspiring Station. Stu Aspinall used to keep his Hereford heifers up there during the summer because they're relatively docile creatures and that cuts down on the complaints from frightened townies out for a wander in the mountains.
But they
are curious and will follow you to see what you're up to.
We were meandering up the valley in no particular hurry, accompanied by a few heifers who were just along for the walk. They'll follow damned near anything that's moving; they're not renowned for their intelligence. Two heavily-laden girls caught up with us and overtook us. The heifers, obligingly, decided that they liked the girls' pace better than ours, and took off with them.
But the girls were nervous of the cattle despite our assurances that they weren't vicious and began to walk faster. So did the heifers. The last we saw of them, the girls were pretty much jogging along as fast as they could, packs bouncing up and down on their backs and everything loose rattling, with the heifers obligingly keeping pace. They'd have been pretty exhausted by the time they reached the Bluff about five miles further on, which was as far as the cattle could go without fording the river.
