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I am Burmese and will travel to Burma from Bermuda. I'll need to transit at a New York City airport just to change flights, without leaving the airport.

Do I need transit visa and if so can I apply online?

Yes, you will require a visa unless you have a different passport to the one you implied. (I assumed that you are travelling on an ordinary Burmese/Myanmar passport and you are resident in Burma/Myanmar.)

Information as of 06MAR16 / 2206 UTC
National Myanmar (MM) /Embarkation Bermuda (BM)
Transit USA (US) /Destination Myanmar (MM)
ALSO CHECK DESTINATION INFORMATION BELOW
USA (US)

TWOV (Transit Without Visa):
Visa required, except for those flying Cathay Pacific (CX)
between Hong Kong and Toronto, via Anchorage (ANC), Alaska:

Additional Information:
- Holders of a valid "C-1" transit visa issued by the USA are
allowed to transit to a third country as long as this trip
is 29 days or less and then transit again, as long as this
trip also takes 29 days or less.

(If you have a British Overseas Territories Citizen passport, issued to residents of Bermuda, then the situation is different and you don't need a visa.)

You can apply online, but you will have to go to an interview at the US Embassy in person to discuss your application. There is a US Consulate in Hamilton.

http://www.travel.state.gov/content/visas/en/other/transit.html

It can take a while for the US to issue visas (often several weeks, occasionally months, one Russian I know was waiting for eighteen months). You should schedule this well in advance.

Bermuda also has direct flights to London Gatwick, which might be more convenient for you.