Culiacán is the capital of Sinaloa state. As the city is of relatively small size, it is reasonably easy to walk to decent hitchhiking spots, but there are buses that will make your day easier. Most (but not all) buses go through the "centro" or downtown through to one or more of the surrounding neighborhoods. If not sure if a bus goes to the centro, you may ask the driver, "¿Va al centro?" and they will be more than happy to answer. You can check out this map of bus routes.
North towards Los Mochis, Ciudad Obregón, Hermosillo
From the centro, take any bus marked "Solidaridad" ("Soli"), or "Cedro", they usually go along the streets Francisco Villa-Juan Carrasco-Gral Rafael Buelna Tenorio-Cristóbal Colón and back up Highway 15. The buses turn into the Solidaridad neighborhood, but don't worry, they come back out north to Rolando Arjona Amabilis Boulevard near to Highway 15 (how near depends on the time of day). Get out as soon as the driver hits this boulevard, because they will begin going south (and turn right on Santa Anita Blvd).
Take the "Aguaruto" bus in the centro, and after passing the airport, there will be a Pemex gas/petrol station and OXXO convenience at GPS coordinates [24.7754N, 107.4737W]. This is the last OXXO for a while, so it is a good meeting place for families going in separate cars, and stocking up on goods; this is perfect for hitchhikers.
South towards Mazatlán, Guadalajara, Mexico City
"Prepa Huertas" and "Toledo" are the most easily accessible buses from the centro, and will take you the closest to the free route to Mazatlán.