To repot a bromeliad grown out of its container, get a larger one that's 2 inches wider with drainage holes. Make sure the container is sturdy enough if the bromeliad is top-heavy.
Use a mixture of 1/2 well-draining potting mix, 1/4 perlite, and 1/4 orchid bark. Place a piece of screening at the bottom of the container over the drainage hole to secure the soil and allow it to drain. Fill the container's bottom with the mix, then place the bromeliad in and fill around the edges. Leave at least an inch of room from the top of the container to avoid water spillage.
Water the plant well. Add it to an area with bright, indirect sunlight and humidity to let it settle into its new environment.