Be aware that NYC and LI are completely different in terms of schools and districts.
The NYC Board of Education
http://schools.nyc.gov/default.htm is a gigantic entity, the largest in the country, with 1700+ schools
LI is split into dozens and dozens of districts, each with just a handful of schools.
http://www.longislandexchange.com/sc...districts.html On LI it's roughly one district per village or town but there are plenty of exceptions to that.
Are there school buses in NYC/LI for HS students?
In LI, yes, within a certain mileage--many districts provide buses for students over 1 1/2 miles from the school, but the mileage depends on the district.
In NYC, no--students get reduced fare metrocards instead. Also I know of groups of parents in Queens who hire private buses to get their kids to Bronx Science.
And also, do HS students in NYC/LI get to CHOOSE their schools, or are they bound to district/zip code schools?
In NYC--not bound by zip code. The application/choice process is crazy, much more complicated than I can explain so I'll defer to someone else who can describe it. Meanwhile here's a link:
http://schools.nyc.gov/ChoicesEnroll...gh/default.htm
In LI--no choice except for public/private, very much bound by zip codes. I think a couple of districts may be exceptions, like Sewanhaka?