The correct spelling is dass, preceded by a comma: when you see ", dass ..." that is your cue to send the verb to the end of the clause. The easiest way is to think of this in terms of certain verbs that can take a sentence (clause) as an object. For example the verb glauben (believe) can take a noun as an object: Ich glaube [dem Lehrer]. I believe the teacher; or it can take a clause as an object such as [der Lehrer hat recht] "the teacher is right" However, as the object of glauben, the clause undergoes a change when it becomes a subordinate clause (basically, a sentence acting as an object of a verb, as in this example). The change involves moving the verb to the end of the sentence: Ich glaube, dass [der Lehrer recht hat]. In your sentence above, the object of glauben is the clause [ich brauche win Fahrrad]. So again, as the object of glauben, we send the verb to the end "Ich glaube nicht, dass [ich ein Fahrrad brauche].
Hope this helps. Let me know if you have any questions.