For just increasing your comfortable riding zone, the simple answer is ride at a speed where you are slightly uncomfortable and after a fairly short while you will be comfortable riding at the speed! There are ways of doing shorter, more uncomfortable segments to achieve the same thing - but all are just forms of making your body uncomfortable for enough time that you body says "OK, he is going to keep doing that so I will adapt."
It is sometimes mentally hard to just ride comfortably uncomfortable without dropping back to plain old comfortable. If you have a bike computer, seeing your speed constantly can make it easier - if you are normally doing 12 mph on a certain ride, do 13 etc. A cadence sensor can help you to just turn the pedals faster, a heart rate monitor can help too. Those enable structured training, too - much more time-efficient ways others have mentioned for increasing performance.
But, the key to riding faster is to ride faster! Uncomfortable at first, soon comfortably.