Some hens will never go broody, others will many times each year. Your chicken is -most- likely to go broody in spring/summer, but it is an unpredictable thing. She may go broody once in her whole life, or never at all.
For now, go ahead and collect the eggs. Check to make sure that they aren't too old, by putting them in a pitcher of water. If they stay on the bottom, they are still good. If they float off the bottom, throw them away. Just use them for food right now, and collect new ones as she lays them too.
In spring, start paying attention to what your hen is doing. If she stays in the nest, puffs up her feathers, and/or clucks and tries to peck you....those are signs that she is getting broody and ready to sit on a clutch of eggs. At that time, you leave the eggs in.
Until then, there is nothing you can do to -make- her broody. Its an instinctive, hormonal thing.
If she's laying blue/green eggs, she's probably the type of chicken called an Easter Egger (because of the colourful eggs).