Where can I buy the hosebib connection locally?

Home Depot sells all this item in the Plumbing Department. Look for the section where tubing is sold, and you'll find 1/4" tubing, Speed Fit ™ (aka John Guest) fittings, and brass compression fittings like the hose bib connector (part A-696):

You will need to install on the hose bib (garden hose-type) threads, screwing it on as tight as you can by hand, just like you would a garden hose to a outdoor bib.  Slide the nut and ferrule over the end of the red tubing, press it into the hose bib connection's compression side.  Slide the ferrule and nut down to the brass threads, and tighten it with a small wrench until it is tight. The tubing will be held in place by the ferrule, which was deformed as it was compressed by the outer nut.  It will crimp into the tubing, holding it fast.  Turn on the cold water and check for leaks. If you see a small drip, tightening the nut a fraction more should stop the drip.