One only needs to inoculate the bag. Depending on the concentration of the syringe, anywhere from 1-5cc' per bag can be used.
If you don't inoculate right away, you can put it in the fridge while you wait for your syringes to arrive. When the oats are about 15-20 percent colonized (white), gently mix the bag with your hands to accelerate the colonization process.
Once the oats have been mostly or completely colonized, one just needs to mix the mycelium in with the coco coir. Once the bag is colonized, or one sees pins of mushrooms starting, one can open the bag and put it in a clear plastic bag (that is also slightly open and or poke holes in the clear bag, to allow for fresh air flow and evaporation of the surface of the substrate spawn mix).
Spray periodically if dryness occurs and after a flush of mushrooms. An alternative is taking the contents out of the bag and putting the entire block in a plastic container (once it's white with mycelium) and allowing fruiting to occur in the plastic tub known as a monotub. When i send these bags out i know that many people are using spores and that can be a contributing factor to contamination (even if one is using a still air box too). Spores and bacteria are invisible to the naked eye and contamination can sometimes happen. Please know that this particular hobby has it's margin of error.
Please don't hesitate to contact me, as i've grown many mushrooms doing it this way. If looking to grow bulk, be sure to message me and i can help you with that as well.