The weight of what is crossing it does not matter, the strength comes from the round shape and being buried the correct distance below grade.
$18 per foot sounds high for new culvert to me. The last plastic culvert I bought was 12" x 20' and was just under $100, with the smooth liner. About $5.00 per foot. The 24" should be just about twice as much.
I would start at $100 if it is lined, maybe $50 if it isn't.
I have carried it on the lumber rack on my F-150, well strapped down. OTOH, I was very picky about how that rack was mounted on the truck. The guy who did it wanted to put the bolts about 12" from the back of the bed. I insisted on as close to the rear as he could drill the holes.