NextBus API.
Transport for United States API is a free Transportation API that requires no API key, is only available over HTTP and has unconfirmed CORS support.

Unified API suite · now live
Geocode an address, validate an email, track a flight or pull stock data with one account, one dashboard and one API key.
Washington Metro transport API
Community maintained, developer-friendly public transport API
Yes. The Transport for United States API is listed in the Transportation category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
No. The Transport for United States API requires no authentication, so you can start making requests without signing up.
CORS support for the Transport for United States API is unknown. Test a request from the browser, and fall back to a server-side call if it is blocked.
No. The Transport for United States API is only available over plain HTTP, which browsers block on HTTPS sites. Call it from a server instead.