Most bromeliads are shade-loving plants, though thrive with a couple of hours of early morning or very late afternoon sun. Sun between 10:00 AM and 4:00 PM is a no-no. During the winter months this can be stretched somewhat, since the sun is so low in the southern sky. I don't know why exposing your plant to sun would have anything to do with the soil staying wet. You should have well-draining soil. Bromeliads derive very little moisture/nutrients from their soil since these plants have fairly limited root systems. This soil is more for anchorage. Bromeliads get their nutrients and moisture through their leaves and more importantly from their "urn". If you are not misting your plant every few days, you need to do so. Plants inside the house are subjected to very dry conditions, and tropical plants like moisture, not dryness.
I would remove your plant from its potting soil and replace the soil with a very well-draining potting soil. This soil can stay somewhat damp but never soggy. Start your misting program and be sure you always keep a bit of water in the urn. Keep the plant away from that mid-day sun.
Now the million-dollar question. Did you get your plant when in bloom? If you did, and apparently the bloom is now gone, is there a pup or two growing from the base of this plant? Once a bromeliad blooms, that plant will always die and the pups are the only way you will have another viable plant. Also, it is important to know what type of bromeliad you have. Is it one where the central leaves color-up? Is it one that puts out a stalk with a spear-like flower? Or is it one where there is a stalk but the stalk will have numerous flowers along that stalk? When we know more about your plant, I think we can arrive at your problem.