I have a similar situation - well water and a softener. I made my first 10 batches with the well water and had variable success. Some were okay, others were meh. I tried mixing softened and unsoftened water (before I learned about the softener/sodium issue). Finally my wife made a comment about the taste of some beer I had made - she said it was "soapy." I Googled that, and there some comments about it being associated with bicarbonate in the water. I decided to have the well water tested by Ward Labs.
It was terrible for brewing. Very hard, very high bicarbonate, too much sodium, almost no sulfate, and a higher than acceptable level of nitrate. My response? I went to the fridge, uncapped and dumped all the homebrew I had. I was done with the well water! I had avoided learning the basics of brewing water and now I had to bite the bullet.
So I did... and now I buy distilled water from the grocery store at about $0.85 a gallon, add my CaCl, gypsum, and Epsom salts in various proportion and the occasional bit of lactic acid. My beers ever since have been GREAT, except for one or two that had issues unrelated to water. It was the best thing I ever did for my brewing.
Bottom line, you can't always tell from the taste of your water. Bad taste would certainly imply a problem, but even good taste can mask issues that affect the chemistry of brewing.