Gurgling noises in drains are normally the result of air being trapped in front of the body of water moving down the pipe. When the pressure builds up the air forces its way past the water, gurgling as it goes. The answer is that you must install a vent in the pipe downstream of where the problem is. Normally, the waste pipe will terminate in a 4" stack which then runs to the main sewer. This stack should extend straight up through the roof of the house and vent to atmosphere. It would be worth looking to see if the stack has been blocked by a birds nest or something similar.
Also, on a double-bowl kitchen sink w/disposal some disposal debris might accumulate on the connected drain pipe between the two sinks. This debris can cause a delay in draining the water which causes a gurgling sound. If you put a few drops of liquid dish detergent in the disposal it will immediately eliminate the problem. However, this is not a permanent fix because debris will accumulate again. The periodic use of the liquid detergent will help to disseminate the debris to cause less of a problem.
Question, having removed one bathroom sink, (double sinks before), now my sinks bubles when as it drain. Can I nstall a air intake on the other drain?