How do I get past the bouncer, and into Speedy's Bowling Alley?

Hint 1 of 6:

The bouncer won't let you in to the bowling alley unless you are properly
dressed.

Hint 2 of 6:

What might be the proper attire for a dark, spooky world?

Hint 3 of 6:

Something black.

Hint 4 of 6:

Possibly a cape of some sort.

Hint 5 of 6:

The Carecrow is willing to trade "Cape Fear" for a new costume.  Cape Fear
may be the proper attire.

Hint 6 of 6:

As you stand in front of the bouncer, use the cape on yourself.