What's the word for something scary but actually harmless?

Solution 1:

Not a single word, but the term paper tiger is used this way, though it also has political connotations due to its origin in Maoist era anti-US propaganda and its continued usage in political contexts.

The meaning isn't an exact match either, since it means "threatening but harmless", rather than "scary" in the horror-movie sense.

From Merriam-Webster:

: one that is outwardly powerful or dangerous but inwardly weak or ineffectual
// The new laws are just paper tigers without any method of enforcement.

Solution 2:

Very close to "bugbear" is bugaboo:

1: an imaginary object of fear

// politicians complaining about that old bugaboo, high oil prices
// doing one's tax returns are a real bugaboo for some people
_{definition from m-w.com}

from Oxford Dictionaries:

An object of fear or alarm; a bogey.
// ‘one of the favourite bugaboos, the ticking biological clock’
_{definition from oxforddictionaries.com}

Note that despite the definition as "imaginary", the quoted usages are about real items that cause undue fear.

Solution 3:

Are you thinking perhaps of phobias? Phobias are only “scary” to those suffering with the actual phobia, or irrational fear— but it’s often the case that most people would not find said phobia to be alarming or disconcerting (if they aren’t suffering also with the phobia, that is)