Presumably by teeth cleaned you mean a dental hygienist clean where they remove dental plaque? My dentist has been a bit lax with this recently, the dental hygienist was pregnant or something.
The mouth can be a big problem. My dentist put a filling in the rear of one of my teeth at the back and I was eating a very hard Goji berry one day which pulled the filling out. I got a dental appointment as soon as I could but my dentist refused to refill the tooth which I am seriously worried about because I have had it become infected on several occasions since and food tends to get stuck in the tooth. Bacteria from the mouth can get into the blood stream and can lead to circulatory problems.
I make yoghurt out of a oral probiotic mint called probiotic smile (ProBiora3) that contains 3 different bacteria which do not produce lactic acid and therefore do not rot the teeth. They produce hydrogen peroxide which can help whiten the teeth, freshen the breath and destroy other oral pathogens. I use an old tooth brush dipped in the yoghurt and work it into the hole in my tooth. I also work it around my guns and floss to get it past dental plaque and work it into the gums to help destroy the harmful bacteria which get into the tooth bed. The idea is that these bacteria do not produce lactic acid so should help stop other bacteria from rotting the tooth destroying competing bacteria with bydrogen peroxide.
I also supplement with Calcium, magnesium, vitamin K and Boron.
Making the yoghurt from one of the mints takes a very long time for the first batch over 12 hours but further batches using a previous batch can be done in around 3.5-4 hours.
One pack of the mints has lasted me a very long time as they are rarely needed once the yoghurt has been cultured. I use low fat powdered milk at a high concentration because it helps the yoghurt set nicely. I have been adding some activated barley, bee pollen and FOS to it. I boil about 5 litres of milk for about 15 mins to sterilize it.
There are essential oils which can be helpful for use in the mouth. Clove bud is one of them. Peppermint oil contains menthol which is known to be effective against plaque. I use Clove bud, Red Thyme (Thymol), Eucalyptus and Peppermint essential oil to treat infections of the mouth. Salicylic acid (methyl salicylate) is also meant to be effective against plaque. I use Euthymol toothpaste which contains several of these components and is without fluoride which I avoid. I like the taste of it too.
For gum bleeding it might be worth getting plenty of vitamin c and biofavonoids. Eating red/blue/black berries might be helpful to strengthen the gums.