Is it a good idea to clean bacon with water before putting it into the pan to remove some salt?

The answer to this is no - the salt in bacon is not generally on the surface, it is impregnated into the meat to cure it. Because of the cellular nature of meat, the diffusion of salts out of the meat is quite slow; washing it in water before or during cooking will not remove substantial amounts of the salt. Having said that, you can lower the salt content of cured meats by soaking them in water for several hours (or boiling when you make stock). How much salt these processes remove depends on the meat type, the salt content, and how much water you are putting them into.

There is some salt in the brine that is often packaged with wet-cured bacon. This would be best removed by blotting with a paper towel; you could rinse, then blot dry. Using water and then placing directly in the pan will affect the cooking process, so that you end up with flabby unappealing bacon.

If you are worried about your salt (usually sodium) intake - try cutting out the bacon, apart from on special occasions. A general lower salt intake will be what you need to aim for - slow reduction in amounts added to cooking or switching to potassium based salts can keep flavors similar to what you are used to.

If it is a matter of taste, @rumtscho has pointed out that frying results in saltier tasting bacon. This may be because the salt is concentrated by evaporation or loss of water within the bacon or because of flavor changes associated with cooking.

Yes, you can reduce the salt in bacon by boiling it. However, I don't know if it will result in a one-third reduction of the salt content.

In French cuisine, when making choucroute garnie (braised sauerkraut with meat), for example, bacon is simmered for 10 minutes in water before being cooked with onion and carrot. This is to reduce the salt content.

For your purposes, it would be best if you had a large chunk of bacon, which you simmered, chilled, then sliced. With already sliced bacon, this will make the secondary cooking more difficult. However, you could place the simmered slices between two foil or parchment lined sheet pans (to keep them flat), and do the final cooking in the oven.

I would start back backing up bob1, much of the salt is bacon is chemically bound in the curing process. You are not going to wash off an appreciable amount. Additionally, many commercial bacon cures are done by "pumping" the cure to process the meat more quickly. Traditionally the bacon is cured from the outside, either with a brine or dry rub, but with pumping the brine is injected at multiple points to cure fast which leaves nothing to wash off even at the factory.

There are low salt bacon brands on the market, and if they fit your taste, they are an option. Personally, I have a low opinion of them, but have only tried a couple of brands. Know though that curing is not always needed. Bacon can be made from fresh pork belly (or other proteins) with no curing at all including little to no added salt. You may be able to find some of these commercially, but because they do not include curing time, they are actually fairly easy to make yourself and since you are doing it, you can control not only the salt, but other added flavors such as if you like a bacon with more pepper or if you like a more lean bacon.

Any search engine should find you a number of such short cut recipes and instructions, but just as and example, here is on from thekitchen.com (no endorsement intended). They call for only a sprinkle of salt and their ideas are just a starting point. Where fully cured and smoked bacon takes me 7-8 days, they are looking at an hour or two for their low sodium approach. (Yes, since I make my own, I am a bit of a bacon snob, but I may try their approach to see if I agree that the taste is spot on.)