The species used in the planting should be consistent among themselves and especially with the species of the accompanied bonsai in terms of environment. Exceptions might work where, for instance, hardy moss represents tropical, a tiny grass represents tropical reeds, etc. But it must appear to be consistent (bonsai is often about deception). Consider tropical vs. native environments, arid vs. forest vs. wetland/rainforest; do the species all potentially reinforce the same conditions? If your bonsai implies or is revealing a seasonal aspect (leaf colour, flowering, lushness) then the companion plants should as well. All species on a container must overwinter together, so must have a common survival zone.

Attempt to reflect the overall style of the main bonsai and environment, including conditions of growth (windy, alpine, lushness, etc.). In some cases the companion actually completes or reinforces the environment or season through flowering, lushness or sparseness, rock vs. moss, etc.  

Some typical situations:

A mountain scene might best utilize short grasses, and tiny alpine plants. 

Warmer climate root-on-rock settings may benefit from moss and trailing groundcovers (e.g. thyme) representing vines cascading downward, even small shrubs and blooming plants could fit. That is, these species may work on a companion plant (not often used with these styles), or on the rock planting itself.

Forest scenes might benefit from shallow companions with forest-edge plants such as grasses, tiny shrubs, ground covers (on rock if consistent with the forest), or wetland material if it’s a shore-side scene. 

A cedar or spruce bonsai could have accompanying ferns and lush wetland plants. Flowering plants might be appropriate if valid for the season. 

Our pines may be best with very limited companions; perhaps mostly moss and small grasses or low shrubs. Accompanying stones often work better with a rocky scene than a companion plant, but a grass-on-rock item may add interest here.