Not sure what you had in mind - a cheaper option than a train ticket? Well, I looked at Transportdirect and a bus journey is possible but requires at least 2 buses, and it would not give me any prices. I also tried National Express and it found no services. I'm not sure what else to suggest!
For reference, 350 to Barton for the Humber Flyer to Cleethorpes. The latter may show as a change from the HF2 to the HF1 at Humberside Airport, but in reality you stay on the same bus. It is registered as two services for legal reasons I don't entirely understand (I believe it is to do with EU regulations and driver hours - but am not entirely certain). Assuming the 350 chosen is operated by Stagecoach (5/6 are), then the full journey would be covered by a Stagecoach East Midlands Day Out ticket, priced at £7.50.Well, I looked at Transportdirect and a bus journey is possible but requires at least 2 buses, and it would not give me any prices. I also tried National Express and it found no services. I'm not sure what else to suggest!