Since they have not bitten you to date, why do you think that they are going to do so? Do you have this fear in general........of being bitten by an animal? If so, then perhaps address this underlying uneasiness with a professional counselor. It goes deeper than those of us here on the Forum can help with.
With regard to cavies in general, keep in mind that they explore the world with their mouths. Unlike a cat, they have little dexterity with their front paws. And, they are prey animals and their natural instinct is to run and hide from everything and everyone. We call them "house eagles"........meaning that they are always vigilant that the imagined scaries are lurking just overhead at all times. Only time, patience, and yes, a lot of handling will gentle and reassure them that you mean them no harm.
It would be very helpful if you would get the cage off the floor! You can make a grid stand to fit or put the cage on a table to raise it. That way you aren't this big hulking creature who may mean them harm. My cage sits alongside my desk on a grid stand which also makes it easier on my back. My cage also has a loft and when the boys are in the loft, they are virtually at eye level with me sitting in my desk chair. This really helped my skittish boy become more comfortable.
It is a good sign that Trixie licks you because in general, that is a sign of affection. Be cautious that your hands don't smell like food until they absolutely know the difference. Cavies get to know you by your voice and your smell which means that you should always speak to them before you attempt to pick them up. With any new and frightened cavy, pick it up and cuddle it on your chest to calm it. My cavies have always known that this is their "safe space" and calm down, but again this means that you have to pick it up to do so.
Being bitten by a guinea pig isn't the worst thing in the world. Even a tame cavy will occasionally make a mistake and bite if startled or frightened. For instance, last evening my Sparky who is the ultimate mellow fellow got startled for some unknown reason and reach out to lightly bite my hand. He immediately realized what he had done and began to lick it as if to say, "I'm sorry Mom.......I didn't mean to do that". Again, a cat probably would have swatted the hand, but because cavies don't have dexterity with their front feet, the mouth was used.
Try wearing nitrile/latex gloves for a while. Although this defeats the aim of them getting to know you and your touch by your scent, it will protect your hands and enable you to handle them more. One of my boys hated getting his nails done and I always wore a glove to prevent bites. He had black nails and it wasn't unheard of for me to cut one too short and cause him pain. Fortunately, that didn't happen very often, but I still wore a glove on the hand that held him.
Not to discourage you, but it can take a very long time for a cavy to learn to trust you. They are as individual as people and some of them are just high-strung, excitable and fearful. If you are fearful, then they will pick up on that. The key is to be absolutely calm and consistent with them. And, yes, you need to handle them.......frequently.
