It is a positive commandment to learn Torah. But the concept of bitul Torah seems to imply that it is also a negative commandment not to learn Torah. Where does this concept of bitul Torah come from?
I don't know of any negative commandment per se, and as @DoubleAA pointed out in the comments, the term bitul does not imply that there is one. As for where the concept comes from, here's one place:
אַשְׁרֵי הָאִישׁ אֲשֶׁר לֹא הָלַךְ בַּעֲצַת רְשָׁעִים וּבְדֶרֶךְ חַטָּאִים לֹא עָמָד וּבְמוֹשַׁב לֵצִים לֹא יָשָׁב. כִּי אִם בְּתוֹרַת ה' חֶפְצוֹ וּבְתוֹרָתוֹ יֶהְגֶּה יוֹמָם וָלָיְלָה
Happy is the man who does not walk with the counsel of the wicked or stand on the way of sinners or sit in the company of mockers; but whose delight is in the law of the LORD and who meditates on his law day and night.
Note what meditating on the Law is contrasted with.
The Gemara in Avodah Zarah (18b) citing the Tosefta (ibid. 2:2 in the Vilna Shas edition) also makes this connection; equating bitul Torah with sitting in the company of mockers.
the verse "ki dvar H-shem baza hikaret tikaret" ("For they have denigrated the word of G-d" (Parsha shlach) which the talmud says refers to bitul torah
It seems that the crux of the question is whether or not there is a general obligation to learn all day (and night). If there is, then one would be "mevatel" this assei by ceasing study (d'chiya notwithstanding.)
See here cited here. where R. Yonah is presented as holding so. The Rambam however is not cited, however (presumably) because in hilchos talmud torah he doesnt say that one must learn all day. Rather he implies (1:8) that one must merely assign time in the day and in the night.
We can infer this from the Chayei Adam (cited above) as well who writes:
וכן בשכיבה אצ"ל שבזמן שיוכל לעסוק בתורה ובמצות לא יתגרה בשינה לענג עצמו
His juxtaposition of Torah to mitzvos is telling. Just as the mitzvos he is encouraging one to fulfill are obviously praiseworthy but not obligatory (kiyumis) (for otherwise it would go without saying that one must perform them rather than taking a nap) so too we can infer that studying Torah is also praiseworthy but not obligatory (besides for the minimal requirement; see Rambam).