How is silica bead bonded into polystyrene?
You can functionalize silica to add polymer "brushes" to the surface. You can also buy pre-made functionalized silica, although the downside to that is it isn't always easy to get the manufacturer to tell you exactly what is on the surface.

This isn't really going to increase the attractive interactions between the silica and the polystyrene, however. Polystyrene has a bulky aromatic ring hanging off of each monomer, and no sites that can participate in hydrogen bonding. When you add hydrophobic brushes to the surface of the silica, what you are doing is limiting the ability of the silica to aggregate due to hydrophilic interactions with itself. As a result, given enough kinetic energy (temperature for melt casting, or sonication for solvent casting) you can get the particles to disperse. Then, if you solidify the polymer quickly enough, they will be kinetically trapped in a dispersed state.

Depending on what your goal is, this could be enough for your application. However, if you want to get the particles to strongly attract to the polystyrene, you aren't going to be able to get much farther than van der Waals interactions. That's a limitation of the polystyrene, not the silica.

Other particles (gold, or carbon nanotubes, for example) will be more hydrophobic and easier to disperse without functionalizing, but you still are not going to get very strong attractive forces between the particles and the polymer.