Translation:He does not want to bike without his mother.
Well, I agree with your general statement, but I don't think that "niet" belongs in that position, rather it should be:
Hij wil niet zonder zijn moeder fietsen.
In Afrikaans, this particular word order is enforced by the STOMPI rule. I suppose Dutch is more lax with the word order, so the infinitive is not necessarily pushed all the way to the back?
You already conjugated "willen" in this sentence, so you don't conjugate the second verb "fietsen". It's the same as in English where you say "He does not want to bike without his mother" instead of "He does not want bikes without his mother". When you have verb phrases like this, you only conjugate the first verb.
Context indeed. Had it been "he does not want the bicycles", the translation would have been "Hij wil de fietsen niet" (you need the definite article + 'niet' behind the noun). Or "He does not want bicycles" (so, bicycles in general, not those specific ones) = "Hij wil geen fietsen" ('Geen' applies to the unspecified noun "fietsen"). And then "He does not want to bike" = Hij wil niet fietsen ('niet' because it applies to the verb)