I think there may have been several reasons why Mr. Bennet was among the first to wait on Mr. Bingley.

He got it over and done with, so he wouldn't have to put up with Mrs. Bennets nagging on the same matter for an extended period. Also, if he postponed it, eventually Mrs. Bennet might get impatient enough to ask Mrs. Long or someone else to introduce them to Bingley, which I guess would be less proper than Mr. Bennet's going. Now he kept the initiative visavis her, so he could vex/surprise her when he liked. Maybe he also hoped Bingley might turn out to be an agreeable acquaintance even to himself. And, though he didn't seem to care for Mrs. Bennet's matchmaking, I'm sure he was enough of a realist to know that the daughters were likely to marry eventually and ought to have a fair chance of meeting suitable mates.