According to Peterson's Arms and Armor in Colonial America he could only find two literary examples longbows in relation to North America. The first is an an anonymous document written to sir Walter Raleigh which suggested he arm 150 of his 800 men with longbows for his trip to the new world. It's not clear whether he actually followed through with this advice, but given that longbowmen were still being used by the English army in the 1580s it certainly seems plausible that some made it to the new world. The second is the incident with Jamestown that you mentioned. In the aftermath of the 1622 massacre the Virginia Company wrote to the English Crown asking if they could spare any equipment. In a short time a scheme was hatched where old arms and armors from the tower of London which were "unfitt for any moderne service here" would be loaded up and shipped overseas where they might still be useful against the Indians. These included old, medieval-style iron skull caps, coats of mail and brigandine, 1000 billhooks, and 400 longbows along with arrows. Ultimately, the colonists took in everything except the bows and arrows which were instead sent to Bermuda supposedly due to a fear that they would be stolen by the Indians.

As for why longbows weren't used much or at all in the Americas. First, by the end of the 16th century longbows were very much considered obsolete weapons by most. Well known veterans were making it clear that they considered longbowmen fairly useless in combat and unable to stand against musket fire whether in a skirmish or in a battle line. A firearm could shoot much farther and hit much harder than the strongest archer, and a gun could be aimed "by rule" rather than "by guess." Laws requiring archery practice remained in place on the grounds that they were good for health and would help keep young men out of brothels and gambling houses, but they were rarely enforced. There would be a couple more nostalgic attempts to revive the longbow over the years, but by and large its military career was over.

Second, firearms seem to have found themselves quite at home in the New England woodlands. Killing a deer or a bear with a bullet was much easier than it was with an arrow, and a musket loaded with goose shot likewise made it much easier to kill small game than it was with a bow (or kill several birds at once). In warfare a firearms were considered much easier to use from behind cover and in forested terrain than longbows were, and they were extremely accurate at the short ambush ranges were most Indian warfare took place. There was also the fact that unlike a powerful longbow, guns could still be used by ill and half-starved men if need be. Really the only issue the colonists had with early firearms was the matchlock mechanism, which required importing match cord and proved to be a source of liability. As a result early colonists started aquiring a surprisingly high proportion of wheellocks, shaphances, and other proto-flintlocks at a time when these were still sort of a fairly expensive luxury item. However the extra cost was apparently seen to be well worth it. Once cheaper, more reliable flintlocks became available, native American tribes started working to acquire large numbers of them for hunting and warfare as well.