You can also skip the subshell invocation of date by using %(fmt)T from bash's printf:

  %(fmt)T -output the date-time string resulting from using FMT as a format string for strftime(3)

The man page provides a bit more detail:

  %(datefmt)T causes printf to output the date-time string resulting from using datefmt as a format string for strftime(3).  The corresponding argument  is  an  integer
  representing  the  number of seconds since the epoch.  Two special argument values may be used: -1 represents the current time, and -2 represents the time
  the shell was invoked.  If no argument is specified, conversion behaves as if -1 had been given.  This is an exception to the usual printf behavior.

With that,

    timestamp=$(date +'%y.%m.%d %H:%M:%S')

becomes

    printf -v timestamp '%(%y.%m.%d %H:%M:%S)T' -1