Which subatomic particles are most involved in chemical bonding

Electrons. They form bonds either by being shared between two atoms or exchanged between two atoms forming an electrostatic attraction between them. If an atom of one chemical has a 'spare' electron in its outer shell, and another is 'missing' one electron - they will bond. Specifically, the valence electrons, which are the ones in the outermost energy level of the atom are the particles involved.