I think the taste metaphor does capture it quite well: while piano and dolce are both “soft” in a sense, they are so in very different ways. p is a shy, fragile kind of soft, in the way a balm mint leaf is soft. But dolce is a thick, embracing kind of soft, more like the way a custard pie is soft. As well as how it's sweet.
So, how do you play it? It's hard to explain, this is in fact one of the things that requires lots of practise to really get the feel. A couple of technical elements that can contribute to a dolce sound are
- bowing sul tasto, i.e. further away from the bridge and almost over the fingerboard. This tends to allow generating a smoother, less harsh sound, if you get the pressure and speed right.
- legato phrasing. In particular, avoid rythmically accenting the start of notes, but don't allow the notes to “wear thin” at the end. In fact, you can try outright delaying the note onsets – start very softly but then let the notes bloom. This isn't something you would do in a mere p passage, that should keep the phrasing as-is.
- vibrato. Here I seem to disagree with Old Brixtonian – IMO dolce can come out very nicely with strong vibrato, only it must not be too hectic. Not too fast or too wide, but thick and soothing. (Whatever that's supposed to mean...)
While you're still a beginner, don't worry too much about really getting a noticeable dolce sound within a piece. More important is that you try out how different the instrument responds when you play it in certain ways, that's what will eventually give you the right sense, feeling, for such nuances.