You do realize we did not write the Blue Bird quest, right? It is an original COAS quest and is unchanged. The whole point is that the Blue Bird is an exceptionally fast ship. If you want to capture it, you need a very fast ship and you also need to destroy as much of its rigging and sails as fast as you can at the beginning of the battle so that you will be able to slow it down.
Use a faster ship. Just because you are in a Class 3 ship, does not mean they are fast...usually just means larger and more guns and more crew. Some ships with good speed and decent guns available in ERAS are the Armed English Merchantman Class 4, Patrouille Frigate Class 5, Light Corvette Class 5, Dunkirker Class 4, Fregates Legeres (very fast) Class 5...there are probably a few more, but those come to mind first.
Also, high navigation only allows you to sail better ship class. Obtain the Increased Naval Speed ship perk for your assigned navigator, or if you have no officer, to yourself.