Is it possible to use $array=() in bash?

Probably the simplest thing to do is just unset them. An unset variable will act identically to an empty array in most contexts, and unset $array ought to work fine.

You can't do $foo=bar ever -- that isn't how indirect assignments in bash work. Unfortunately, while being able to do indirect array assignments is an available feature in ksh93, it isn't a formally documented available feature in bash.

Quoting BashFAQ #6 (which should be read in full if you're interested in knowing more about using indirect variables in general):

We are not aware of any trick that can duplicate that functionality in POSIX or Bourne shells (short of using eval, which is extremely difficult to do securely). Bash can almost do it -- some indirect array tricks work, and others do not, and we do not know whether the syntax involved will remain stable in future releases. So, consider this a use at your own risk hack.

# Bash -- trick #1.  Seems to work in bash 2 and up.
realarray=(...) ref=realarray; index=2
tmp="$ref[$index]"
echo "${!tmp}"            # gives array element [2]

# Bash -- trick #2.  Seems to work in bash 3 and up.
# Does NOT work in bash 2.05b.
tmp="$ref[@]"
printf "<%s> " "${!tmp}"; echo    # Iterate whole array.

However, clearing is simpler, as unset $array will work fine.