Welcome to FSM Auto section!
As long as the paint is dry there is no problems masking it of and paint another colour. Make sure to use a good tape with not to strong adesive, I prefer Tamiya masking tape that comes in a variety of widhts and hardly ever bleeds under if properly applied. The easiest way to make a chrome bumper is to use Alclad2 chrome paint, it's a real killer product and I can't understand how I survived without it before.
Front and rear bumpers on my Impala is done with Alclad2 chrome...
...and I'm more than satisfied with the results.
As for which order to assemble and paint that differs from time to time. But I tend to put together as much sub assemblies as I can and then paint them before joining the lot together.
Don't know if I'm making any sense, feel free to ask again if you wan't to know anything else or need to get anything of this clarified.
Good luck!
Niclas