Usually acquired. Aortic regurgitation is usually an acquired disease. Some forms of congenital vascular disorders are associated with aortic valve problems such as Marfan's Syndrome and this can involve the aortic valve. This is rare. Marfan's is inherited in an autosomal dominant pattern. Even more rarely it can also occur as a spontaneous mutation in someone who has no family history.
AI. I am not aware of ai being genetically linked and can't find anything on line to point to say bicuspid valve inheritance as dominant or recessive.