I've called this page, "bow fingers and sensitivity" because it is easy to become desensitized to your bow fingers when you are focusing on other aspects of playing the cello. You can easily become unaware that you are squeezing the bow. Beginners often squeeze their bow fingers and this is BAD! The string takes the weight of the bow and once you are moving the bow on the string, you have to trust that your bow does not need you to hold it. The bow only needs you to guide it and to transmit weight. Go to Transmitting Weight into the String to find out more about this vital concept.
In addition to the sensitivity of your fingers, there are the sensitivities related to being in touch with all of the muscles in your body and also the sensitivity of listening to all of the aspects of the sound you are producing. That's why playing a musical instrument uses more of your brain than any other activity!
When starting out, it is best not to use the bow until you've spent time with just the right hand learning to hold the bow and learning to manipulate it with only the right hand fingers. Do some gentle finger taps to wake up your sense of touch in your fingers. Even if you're more advanced, just touching and stroking your thumb against the fingers before starting to practice can wake up the sensitivity.
"Feeling Awareness" is an essential quality which most of us need to cultivate. We are born with curiosity and sensitivity, but these natural inclinations can get dulled down by stressful environments or unhealthy lifestyles.
CelloBello is an excellent website for cellists of all levels. Here is Paul Katz talking about noticing tight muscles and giving very good advice about noticing how your body feels.
I highly recommend that you buy some squidgy rubbery pencil grips to put on your bow to make it more comfortable to hold the bow and so your thumb can feel more secure and flexible. Many professionals use them - they are not just for beginners. Not all pencil grips are the same and you want the kind that go on easily, and don't have any bothersome ridges. I recently bought Paper Mate Foohy Gooshy Grips (73740) from Amazon. They work well (and seem to last - some brands disintegrate quickly) but every year or so they create slightly different shapes - the old shapes go out of style and I get disheartened when I have to buy a package and can only use some of them. Anyway, I usually cut them either in half or I cut 2/3 off to put on over the "bump" of the frog. I don't like to have too much covering on the frog or bow stick. It can dull the sensitivity that you want to have! This video shows how to put one on your bow:
Sensitivity to sound is part of musicality. Lastest research has found that musical people have an abundance of auditory pathway genes. It seems that we have high sensitivity in the inner ear and refined sound processing in the brain.