Drinking dry (aka not sweet) wine is an acquired taste like anything else, but I think it's a lot more accessible than something like getting into drinking neat scotch.
Perhaps you'll never like drinking dry wine, but if you're going to give it another shot then don't start by trying something that's trash. The lower quality dry reds and whites are going to emphasize some of the worst notes which probably turned you off of them in the first place (i.e. they're not rounded, have too much alcohol burn, too much or too little acid, too much or too little oak or tannin, other off aromas etc).
Keep an open mind and try a higher quality pinot noir. It's lighter body and lower in tannin, which is the "bitter" taste that you're referring to. When you say tart I doubt that acid is a problem for you considering Riesling has pretty high acid. Other than pinot noir, I suggest trying an Amarone, garnacha, barbera, cab franc, malbec, or cote du rhone. Don't start with a big bold expensive cabernet sauvignon.