From the M1 Jcn 15 follow signs for Northampton on the A508, which turns into the A45 after going over a large flyover. Billing Aquadrome should be clearly signposted and the entrance is located just off the A45. Billing is about 4 miles from the M1.
From the A1 going south take the A605 from Peterborough, which turns into the A45 at Thrapston (A14 jcn), and follow the A45 for 35 miles all the way into Northampton where you follow the signposts as above.
From the A1 going North your guess is as good as mine. You could try the A421 at Tempsford going towards Bedford, and then take the A428 from Bedford right up to Billing. Its about 28 miles and goes through Bedford but is about the most direct route from the A1.
Zee.