Not sure sounds like reflux.
Are you using or have you tried a raised feeder?
How long has this been happening if like forever I'd go with reflux its so common and often goes unnoticed.
It could also be a nasal issue or symptomatic of CT but you'd see or notice a few more symptoms-if it's not just beard drips though it's a sign something is going on.
I use a water bottle ell okay try to use a water bottle for my miniature schnauzer, sometimes she drinks from the boys' bowl, but schnauzers are supposed to drink from bottles because of issues with their double coat beard and year and bacterial infections and beef staining.
I'd just be sure to minimize the amount of water at one time if possible & use a raised feeder see if it stops first IMHO
Most Yorkies use a 4' mine use a 7' they are taller, see if that alleviates it but to be totally straight forward honest everyone should be using a raised feeder and water bowl for your dog's comfort.
Here's a link to the ones I buy because they are so inexpensive and definitely stylish, well made yes I just love these. Seriously though I should get a percentage of sales because I've talked like 20+ ppl into buying one I have 7!
Shabby Chic Pet Feeders - The Bella Cottage