For an adapter check your local hardware store. Basically you can use compression fittings meant for soft copper, but you must use brass inserts to keep the tubing from collapsing. They fit inside the tube and have a flange on the end. We sold these at the hardware store I worked at for years in the plumbing section.
Before you do that though, if your hose is the clear type and not the milk white, try heating it and forcing it onto the larger fitting. 1/8 to 1/4 would be a stretch, but I've seen that stuff be forced onto many a barbed fitting I would never have believed it would have made it. Multiple attempts at heating with a cigarette lighter held below at a reasonable distance from the flame and pushing onto the barb just might do it.
Bill