The mining arena in the Edgeville dungeon is not very close to a bank, however the ladder (south of the mine, just before the hill giants) will bring you somewhat close to the Varrock west bank. Alternatively, if you have the Varrock Armour 3 you can use the Cooking Guild's bank. Remember that you will need a Brass key to pass through this door, which respawns west of the ladder. Alternatively, the ladder (on the western side of the dungeon) will take you up near Edgeville's bank. It is not recommended that level 3 skillers mine here.