There is a couple of ways you can do the convert. High Quality uses the existing zerk grease holes and you route the copper tubes out in the open. If you want to make it look modern you plug those holes with pipe plugs and drill new holes inside the saddle and route the tube inside it. Bridgeport uses a 1/4" x 3/8" lead tube that squashes around the copper tube to hold it the tube into the drilled hole (special order). I sometimes just epoxy them in. But with either method you need to clean out the old grease by dismantling the machine.
Some use the existing zerk fittings and use way oil instead of grease. You need to but a old style grease gun with oil (there was a thread someplace where they talk about special grease gun that are made for oil that you can still buy.
Back in the old days, before they made grease cartridges and when you sucked or scooped the grease in the gun, you could use those grease guns to pump oil. Basically they had a leather or rubber cup that sealed the piston. The new ones leak like a sieve. If your drilling the new holes you're introducing chips and you have to dismantle it. I would do it with the High Quality type too.
I use to sell Trico Oilers and when I took the sales class the Lubrication Engineer taught us to never mix oil with grease or mix greases as some chemicals (waxes in lubricatants) have a hardening chemical reaction that gel and plug the system. Another thing you have to think about some of the old Bridgeport's had a relief milled in the middle of the saddle sometimes, aprox. .030" and you can't go to oil as the grease acted as a barrier or seal to keep the chips and coolant out.
You can check that by checking the middle 1/3 of the table and saddle ways. If your rebuilding the machine you could mill that out, grind in some new oil grooves or epoxy Rulon on the ways. It's a good practice that every Bridgeport owner makes it a weekend project to pull apart the machine and clean it. The feed nut brackets get plugged. So pulling it apart and blowing out the crud. You will be amazed how the inside of the knee gets full of chips. Bridgeport's are simple to pull apart.