One great way to bond and have a quiet moment with your cat is to practice cat grooming. Cats generally take good care of themselves as far as cleaning and picking out dirt and debris, but they don't usually object, and actually quite like a soft brushing and cuddling with their owner.
Get yourself a cat brush (don't be using your dogs brush as the bristles are harsher and bigger) and you can try sitting your cat on your lap or get down on the floor with her and gently brush her.
Starting with the areas that she has a hard time getting at, such as the back of the neck. If your cat wears a collar, either get under it or take it off while practicing your cat grooming. Your cat should start purring, and enjoy these moments.
Brushing loosens older fur underneath and any dirt and debris that she could not pick out. She may even roll over for you and let you brush her tummy. I have found that even the most aloof cat will give in to a good brushing, and start purring, and enjoy cat grooming.
But at the same time, she will tell you loud and clear when she is done. I have a cat that will let you brush her on your lap for about 10 minutes, then suddenly she is off. But during that time she is purring and rubbing up against me. Normally she is quite aloof, so this is a nice time to bond with your cat.
Cat grooming, also gives you the chance to check her out closely, make sure that everything is OK, that there are no sores or bald patches you need to be concerned about.
If you use a proper cat brush when practicing cat grooming, there should not be a flutter of fur in the air, the brush will catch it. Just make sure and empty and wash the brush afterwards. But you will see a instant difference in the sheen of your cats coat with cat grooming.
Cat grooming usually included nail clipping. Now this can be a tough one. If you started clipping your cats nails from when they were a kitten, you may be able to get away with it, but most cats don't like having their feet, or their nails touched.
One tip I found to be a good one, was to wrap your cat in a towel, with a foot sticking out, and have one person hold this towel under their arms and quickly just clip the points off the nails.
Another way, was to have a person sitting with a thick towel on their lap (don't want panicked scratches!) and basically have the cat in a sitting position then hold the cat under its armpits, so that their front paws are sticking straight out. You have to be quick, but at the same time you only want to clip off the point, or it will hurt them.
Unless your cat has fallen into some nasty mud puddle or sprayed by a skunk, you don't usually need to bath a cat. But sometimes they can get so dirty or full of fleas that this is necessary. In this case you have to have help.
Put a leash on the cat collar so you don't lose your wet cat through the house!. Then grab them by their scruff and basically give as quick a wash as you can and watch out for their eyes, then quickly put them in a soft towel and rub dry. Then give them a treat and let them go.
They will finish off the drying for you! They will lick their scent back onto their fur. If you are not sure about bathing a cat, check out you tube for washing a cat videos, they can be helpful.
Cat grooming for the most part, is a great way to spend time with your cat. With regular brushing and nail clipping, and monitoring their health, you can keep your cat healthy for a good many years.