A recumbent bike will not work for spinning - spinning involves a lot of jumps, standing climbs, etc. Things you do out of the saddle and standing up, which a recumbent does not allow.
Linda, I know you won't be able to use the workout as it is designed but maybe you could modify it by doing some of your own moves when she does things you can't like jumping/ standing??? Pedal backwards, sprint real hard, heavy, heavy tension hill or whatever. Or, you have a wonderful Christmas or birthday gift for a close friend!
From what I am reading through out the other forums and facebook, you pretty much need a spin bike. Which really is a bummer for those of us that don't have one. I'm sure the workout will be great for whomever is fortunate to have a spin bike.