I was tempted to start by saying that the common couch grass (Elymus repens) must be Dorset's most common grass species but on reflection that might not be a fair assessment. Indeed, just how do you decide what our most common grass species is and what appears to be a simple question becomes more complex the more I think about it! As always the issue comes down to habitat, specialisation and adaptability.
Couch grass tends to be a species of cultivated land and is sewn in meadows for hay production. It is a vigorous plant that spreads by deep rhizomes. You can try and dig couch out but leave even a small fragment of the rhizome in the ground and guess what - you have more couch grass growing! These two factors mean that couch is abundant around arable land, pasture meadows and amenity grass areas where it has been sewn and it is very common anywhere near one of these habitats because of its ability to spread. It is a very, very common grass. However, away from these 'artificial' habitats the position changes and you will find very common grasses on chalk soils, others on acid soils, others in damp meadows and so on. Some grasses are more widespread and found in more places than couch, cocks-foot and Yorkshire fog for example.
I guess the answer to what is the most common grass in Dorset rests with the total number of plants of each species in the county. It could be purple moor grass or tor-grass, it might be cocks-foot or Yorkshire fog, it could be annual meadow-grass, it may be couch but who is ever going to try and count the number of plants of each of those? I am sure all would reach the billions.