During your stay in the hotel the best transportation option is by subway. The gate B of the Catete Subway Station is located just few meters from the Windsor hotel. It is very easy to find taxi cabs around the hotel and Uber works well in Rio.

From the Tom Jobim International Airport

Unfortunately, usual public transportation does not operate well at the Rio International Airport. There is no direct line and available options take too long to arrive in Downtown or in the Hotel. Uber does not operate at the International Airport.
We suggest two options.

Taxi companies:
Usual taxis (yellow): Ground floor (there is a queue outside the terminal). Two cooperatives operate at the Airport (Aerotaxi and Aerocoop)
Special taxis (other colors): Company booths are located inside the passenger lounge (next to luggage belts). Prices are higher than yellow taxis.
Special bus:
A special bus line (n. 2018) goes from International Airport to the South Zone. It stops at Santos Dumont Airport. Those who are going to the Windsor Hotel must ask the driver to stop at Praia do Flamengo near to Palacio do Catete (Ferreira Viana Street).

From the Santos Dumont Airport

Santos Dumont Airport is integrated to the public transport network through VLT (tram). Those who are going to Windsor Hotel can take the metro in Carioca (lines 1 or 2 direction Botafogo or Praça General Osório). Yellow and Special taxis operate in Santos Dumont. Uber cabs can be taken at the Bossa Nova Mall (an Airport Extension).