In reply to davy_boy:
Cycling specific jackets are worth having, but it sounds like your hardshell is a better fit than your cheapo cycling top.
Cycling jackets should be longer at the back and arms to allow you to stretch out on a bike. some have a backside flap to keep your bum dry.
The biggest difference, and one tha you might struggle with the hadshell is the amount of heat an sweat you generate when cycling could get you wet under the hardshell.
I wouldn't wear your hood over your helmet - it will act like a very effective air brake.
If you must wear it, put it under your helmet, but personally unless it's really cold (sub 5C) i would avoid it as it's horribly restrictive to your hearing (even at low temps I just use a wool skull cap type thing)
And Mountain hardshells tend not to have all the reflective piping etc that you find on cycling jackets for safety/visibility
Post edited at 12:02