How can I redirect the output of the "time" command?

no need to launch sub shell. Use a code block will do as well.

{ time ls; } 2> out.txt

or

{ time ls > /dev/null 2>&1 ; } 2> out.txt

you can redirect the time output using,

(time ls) &> file

Because you need to take (time ls) as a single command so you can use braces.