Baking 0603 Components
The reason to bake them is so they are not damaged during the solder reflow process. Running them through the oven after mounting them on the board would defeat the purpose.

If you are hand soldering, don't worry about baking them. They are not particularly more likely to be damaged due to moisture ingress than they would be due to the simple uncontrolled nature of hand soldering. 

If you are reflowing then I would expect you can bake them in their tapes. Generally I've only heard of prebaking being done at professional assembly shops. At which the process of de-taping them and then re-taping them would be more expensive than simply discarding the parts and buying new ones.