In the USA, there is no federal law that expressly prohibits bribes in a commercial context ("commercial bribing"), but there are laws in many states - so it depends on the state. Most states do have laws about it.
For example, the law in the state of New York is quite strict. What you describe would qualify as "commercial bribing in the second degree". You would be liable under § 180.00:
A person is guilty of commercial bribing in the second degree when he
confers, or offers or agrees to confer, any benefit upon any employee,
agent or fiduciary without the consent of the latter's employer or
principal, with intent to influence his conduct in relation to his
employer's or principal's affairs.
Commercial bribing in the second degree is a class A misdemeanor.
New York Penal Law § 180.00 - Commercial bribing in the second degree
The employee receiving the bribe would also be liable, under § 180.05 - Commercial bribe receiving in the second degree:
An employee, agent or fiduciary is guilty of commercial bribe
receiving in the second degree when, without the consent of his
employer or principal, he solicits, accepts or agrees to accept any
benefit from another person upon an agreement or understanding that
such benefit will influence his conduct in relation to his employer's
or principal's affairs.
Commercial bribe receiving in the second degree is a class A
misdemeanor.