You can do that with
sudo, no need for both.
sudo -H -u otheruser bash -c 'echo "I am $USER, with uid $UID"'
The relevant parts of
-H The -H (HOME) option requests that the security policy set
the HOME environment variable to the home directory of the
target user (root by default) as specified by the password
database. Depending on the policy, this may be the default
-u user The -u (user) option causes sudo to run the specified
command as a user other than root. To specify a uid
instead of a user name, use #uid. When running commands as
a uid, many shells require that the '#' be escaped with a
backslash ('\'). Security policies may restrict uids to
those listed in the password database. The sudoers policy
allows uids that are not in the password database as long
as the targetpw option is not set. Other security policies
may not support this.
su can only switch user without providing a password if you are root. See Caleb's answer