(a) Rashi in Shabbos (25a) holds Nosar does not necessarily need to be burnt. This is because Rashi understood that when the Torah says to burn Nosar it means that Nosar shall be destroyed. Any method of destruction is acceptable as long as the Nosar will cease to exist. Tosfos (ibid.) disagrees with Rashi and holds that Nosar must be destroyed by burning.

According to Rashi, we need an explanation for the Gemara in Pesachim 27b where the Chachamim reply to Rebbi Yehudah that if he did not find wood he will refrain from destroying the Chametz. Surely he can still destroy the Chametz by other means. The Chasam Sofer (OC 104) answers that since other methods of destruction take time, they are unacceptable since every second that the Chametz is not destroyed its owner transgresses a prohibition. This is true despite the fact that when the Chametz is eventually destroyed, the prohibition is considered to have been rectified retroactively. The Chasam Sofer explains that this is unsatisfactory, because nevertheless at the time he would be transgressing a prohibition.

We can infer from the above, as far as Nosar is concerned, that if one did not have wood (or other fuel, see Minchas Chinuch 143) with which to burn the Nosar, according to Rashi he would be required to destroy the Nosar by any other method possible. However, according to Tosfos he would have to wait until he found fuel, since destroying the Nosar any other way would mean that he had not rectified the prohibition of leaving over the Kodshim. If however he knew (or suspected) that he would not ever be able to destroy the Nosar in a way that constituted an upholding of the Mitzvah of destroying Nosar, he would be better off destroying the Nosar by any available method as soon as possible, so as to minimize the time he had transgressed the Issur of Nosar.

(b) There is no specific time within which Nosar must be burnt, but one should do so as soon as possible in order to minimize the time spent transgressing the Isur, as explained above.