Mysore to Srirangapatna distance is about 20km. Srirangapatna island makes a great excursion from Mysore.
Mysore to Srirangapatna by Bus Take any bus heading towards Bangalore from the KSRTC bus stand. The bus can drop you at the Srirangapatna town square near at the state highway side. It's a 20-30 minutes bus journey. From here take an auto-rickshaw to the attractions on either sides of the highway. They are about 2-3km from the highway.
Another alternative is to take a city bus from the Mysore City Bus station located at the corner of the Mysore Palace. There are both AC (Volvo) and regular bus services to Srirangapatna. Some services goes all the way to Gumbaz.
Mysore to Srirangapatna by Driving Head north of Mysore city towards Bangalore. You can even take the Outer Ring Road. Turn to wards Bangalore direction. You'll cross the Kaveri River where the Srirangapatna town square is located. Turn left for Sri Ranganathaswamy temple and other attractions around the Srirangapatna fortification like the Water Gate,Tipu’s Death Place , Masjid-e-ala, Bangalore Gate,Flag staff Cavalier, Mysore Gate, Obelisk etc
Turn right from Srirangapatna town square on the highway for Gangam, Gumbaz, Tipu's Summer Palace , Nimishamba Temple etc.
It's a 10-15 minutes drive from Mysore city to Srirangapatna town.
Mysore to Srirangapatna by Train This too is an option, a very cheap option if you travel by one of those Mysore to Bangalore passenger trains. Srirangapatna railway station is located on the northern tip of the island, very next to Sri Ranganathaswamy Temple. From railway station you can walk to much of the attractions located on the northwestern part of the island.
For attractions located across the highway like Gumbaz, Tipu's Summer Palace , Nimishamba Temple etc. take an auto rickshaw from around the railway station or Ranganathaswamy temple. Check out also the Mysore to Bangalore Train Timings.