The best way to keep your parrot from biting your face when it's on your shoulder is by avoiding your bird on your shoulder in the first place. Does that mean that you should never have your birds on your shoulder? Well, most experts, once you've done plenty of research on this topic, would suggest against having your bird on your shoulder.
Some of the reasons why many professionals are against birds are because:
Shouldering your birds leads them to think they are dominant to you
You can't see your parrot's body language
Your bird is very close to your face
There really is not a black-or-white answer to whether you should allow your bird on your shoulder because the truth is that whether your bird can safely be on your shoulder depends entirely on your bird. If you have a bitey, unpredictable bird, don't let him on your shoulder. You might get hurt badly. It's really just that straightforward.
With my birds, Blossom is not allowed on my shoulder right now because she doesn't come off when I ask her to. My basic rule of thumb is that my birds can be on my shoulder if they come off the first time I ask them. For instance, if Kiwi or Edward puts themselves on my shoulder, they step up whenever I ask them.
Blossom has some difficulty understanding personal space. Although Blossom has never bitten me and loves being very close to me, she doesn't like or understand why sometimes I don't want her up there.
Currently, my shoulder training right now is literally just going to be avoiding her near my shoulders. If she does end up on my shoulders, I target train her to come off. Luckily, Blossom has been very good at listening to my cues.
If you have a bird who either bites or refuses to get off like Blossom, there are few techniques that you can use to target train them. Some helpful tips are:
Hold your bird's feet firmly if they try going up your arm
Offer something to keep your bird busy, like a favourite toy, so they don't get distracted and go on your shoulder
Stick to a routine. If you "every so often" the only target train them, your bird may have difficulty understanding its boundaries
I hope these tips can be helpful for you and your birds!