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I vote for
test -d "$dir"/.
This fosters an autofs mount or an AFS volume mount, so is as safe as an actual cd. No need for an additional test -x.

You can also try:
if ( cd "$dir" 2>/dev/null )
then # do something
fi
If you want the diagnostic from cd if the cd failed, drop the redirection, or if you want a custom diagnostic add an else...

A process can "cd" into a directory when it has execute-rights on it. Test simply if it is a directory AND if the x-bit is set for you:

if [ -d "$dir" -a -x "$dir" ] ; then
# do something...