Both baking soda and ammonia will increase pH. I think the idea behind this, apart from 'recovering' the bath from too low a pH, is that the halide salts (iodide & bromide salts) dissolve easier at a low pH and this, in order to get rid of them, you'd have to raise the pH so they can precipitate out. Sunning helps the volatile compounds (alcohol and ether) to evaporate. In terms of pH, there's not a whole lot of difference between using bicarbonate or ammonia since both will raise pH. However, silver ions end to want to form salts and not all of those are soluble, which can result in loss of silver through precipitation. To an extent, this can often be countered by adding an acid (esp. nitric acid), but it becomes kind of a tricky balancing act of maintaining the right pH.
before experimenting with these methods
My suggestion would be: don't. Most practitioners will tell you that there's no need to muck about with your silver bath too much, and as far as I can tell, they're right. Periodically sun the bath. Filter it if there's stuff floating around in it. Maybe check pH and adjust it slightly if you want to keep it in a specific bandwidth, although plenty of wet plate photographers don't even do this. I would not recommend boiling the bath, adding carbonates, hydroxides etc. in attempts to 'clean' the silver bath unless it's absolutely necessary (i.e. the silver bath has gone hopelessly ineffective and is basically beyond recovery to begin with).
It's very easy to destroy a silver bath this way, which is an expensive exercise. Been there, done that.
my bath turned cloudy after I added distilled water, and I suspect that iodides or bromides may have precipitated out. I used the same distilled water for a new silver bath, and there was no cloudiness, so I don't think the water is the issue.
Distilled or demineralized water? There's a big difference, especially in this context. Demineralized water (which is what's usually sold in supermarkets etc. for household purposes) can be loaded with chloride ions as a result of ion exchange processes used in demineralization. It's actually quite common to see demineralized water being sold under the name 'distilled', even if it's not actually distilled water. Note that the formation of silver chloride depends on pH to an extent; at neutral pH, this will readily form, but in a solution acidified with e.g. nitric acid, this cloudiness may not form. So the fact that you saw cloudiness in one instance and not another in itself doesn't say much about where it came from.
Also keep in mind that adding water to an already watery solution that contains some halides, will not cause halides to precipitate out. So the most likely cause of the cloudiness you saw really was the formation of silver chloride due to the presence of chloride ions in the water. Apparently the bath you added the water to was not very acidic at that point; is this correct?
If it ain't broken, don't fix it!
