I've had a dairy calf suck on my fingers more than once and by more than one calf. Been close enough to a pet steer to give him a good rub-down just about daily. I've been close enough to a cow to milk her or put the milk machine on her...actually done that twice to around 50 cows at one time. Even did that to a Simmental beef heifer that was keen on accepting her calf but her calf was too weak to suckle. I've been close to steers on many, many occasions to feed, vaccinate, deworm and dehorn them, and to walk in the corral to check on them and look for any un-castrated steers, otherwise known as bulls. I've helped calve out a cow, rub down a new baby calf to get it started breathing again and moving, helped with C-sections, perform surgery on a steer with a massively infected scrotum, and do castration on bulls. On numerous times I've helped with semen testing bulls, often being the one holding the tail over the device that gives bulls the necessary "encouragement" to ejaculate for the vet to get a sample. I've even done rectal-palpation on a few cows too, and examined a fistulated cow, reaching into her rumen to get samples, and that sort of thing.
So how close have I've been to a cow? Well, close enough to say I've just about "done it all." This may sound wrong to some of you, but I've been close enough to a cow that I've been in front, behind, beside, inside and outside of one on far too many occasions to count! :)