Hey, I don't bike, I just do treadmill (walk/run) and strength training. And for some reason, I always feel better doing the treadmill first... I think because it is good to get your muscles warmed up before you do the intense strength training. But honestly, I'm not sure if I've read this somewhere, or if I just sort of came up with it on my own.

But it works for me for now, so...
Occasionally, depending on circumstance (since i live with 2 other people) i modify it and do, say, half my treadmill time first, then go to weights, and then go back and do some more treadmill time. But in general, I always do cardio first.
I'm not sure that it would make a difference in the order that you bike and run... but hopefully there will be some other people with more similar experiences to share their ideas