The bowl of water with 4o - means it can be washed at 40 degrees or less
Square with circle is a tumbledryer - cross means it can't be tumble dried.
Can be ironed on number 2 heat setting or less.
You could handwash it first and if it is still grubby then spray worst bits with precleaner and put on a 30 or 40 wash. Or you could put it in the handwash or woollen wash in your machine which is more gentle than a normal wash.Putting it in a pillowcase will also help protect the buckles.
Most cotton bags I have washed have come up well in the washing machine but NOT if they have any cardboard/firm base in the bottom.