Try the following:
s=$({ time dd ... > /dev/null;} 2>&1)
Chepners' answer gave me inspiration, perhaps better:
s=$(exec 2>&1; time dd ... > /dev/null)
$() , . exec 2>&1;, stdout , , time , , , time. exec time, , , . exec, , forked-, .
, , , > /dev/null time /dev/null, , time .