In addition to the family introductions, who are his friends? Do you still remember the place where we first met? Have you tried flirting with a stranger online? Which member of your family were you closest to as a child? Present your most attractive self by practicing good hygiene and grooming.
If I'm feeling particularly outgoing, I go with more casual friends so I'm more free to meet people and do my own thing.
You can ask a second time fairly soon, then if they still say no, give it some time before trying once or twice more.
If she returns your glances and smiles, she may also be interested in you.