According to the MTA , there is Roosevelt Island F Train Service to and from Manhattan this weekend. Also, Roosevelt Island E Train service to an from Manhattan.
Keep your nose and mouth covered while riding with us. You’re helping stop the spread, and taking care of your fellow riders. pic.twitter.com/aWQpmRzA7cNYCT Subway. Wear a Mask. Fill out the Census. (@NYCTSubway) September 3, 2020
“The MTA is in a free fall. The only way to stop it is congressional action, and time is running out.”MTA. Wear a Mask. Stop the Spread. (@MTA) September 1, 2020
Our CEO Patrick Foye teamed up with @transportworker President John Samuelsen to write this op-ed. Its worth your time.#SaveTransithttps://t.co/A3CVcxUjRY
We think OMNY looks especially sharp in F Train orange https://t.co/vIYSDBrbxAMTA. Wear a Mask. Stop the Spread. (@MTA) September 1, 2020
There is a Roosevelt Island Tram Cabin 20 passenger Covid-19 Social Distancing limit. 
According to this Roosevelt Island Operating Corp ( RIOC ) Labor Day Advisory:
… Tram – Will run on a weekday schedule with both Trams operating and adhering to social distancing with 20 passengers per Tram cabin. There will be no Tram Shuttle Bus. See schedule info at: [rioc.ny.gov/302]
Red Bus – Will run on weekday schedule. There will be no Octagon express bus. See schedule at [rioc.ny.gov/368]
Here’s the NYC Ferry Roosevelt Island Astoria Route Schedule which now extends to East 90th street on the Upper East Side. 
Also, Roosevelt Island has a new transportation option with the recent addition of Citbike docking stations.