tyrant (noun) - to refer to the person
tyrannical (adjective) - to describe a person's tendencies
No, I don't mean these words in the sense of a Mussolini or Stalin, but generally for a person who exercises power harshly over those to or for whom they are responsible, sometimes subordinates.
tyrant
noun
3.An oppressive, harsh, arbitrary person:
My boss is a tyrant.
American Heritage Dictionary
1.1 A person exercising power or control in a cruel, unreasonable, or arbitrary way.
* ‘her father was a tyrant and a bully’
* ‘Some are very gentle, polite, and accommodating during the workday to clients and customers, but when they come home they become
demanding and unyielding tyrants.’
Oxford Living Dictionaries
It's actually tricky to get good definitions of these words because it usually goes something like:
tyrant = One who is tyrannical
tyranny = Something tyrannical
tyrannical = Characteristic of a tyrant or tyranny.
So we have a bit of a loop here. However there are some definitions that are useful:
tyrannical
adj
2.Characteristic of a tyrant or tyranny; despotic and oppressive:
a tyrannical supervisor.
American Heritage Dictionary
Of course these words don't describe people who are particularly susceptible to becoming tyrants once endowed with greater power or authority, but this is the closest I could get. I'd be interested in knowing if there's a term, maybe a psychological one, for a person who can easily let power go to their head, as you say.
Also, I know you're looking for a single word, but the idiom "drunk with power" contains within it the meaning that the person has become bossy after gaining authority or power.
One dictionary (Oxford Living Dictionaries) has an entry for "power-drunk", but no others do, so I wouldn't use it outside an informal context.