I happened to have been reading the part of the Talmud (Tractate Pesachim) just yesterday where it discusses the issue of chametz (leaven) owned by a non-Jew who rents a residence (even a room) in the home of a Jew.

There are three source mitzvot in the Torah that are of concern here (I'm eliding them): "…yet on the first day you shall remove leaven from your houses…" (Exodus 12:15), "Seven days shall there be no leaven found in your houses…" (Exodus 12:19), and "…and no leavened bread shall be seen with you…" (Exodus 13:7). The penalty for transgressing these is getting "cut off from the Congregation of Israel". I've heard a Rabbi say that this is basically the only thing that can get you excommunicated from Judaism, so it's a very serious set of mitzvot.

I'm working from the Steinsaltz English translation, PI 5B-6A (pgs ~23 - 28). The Talmud being the Talmud there's a lot of back and forth. The gist of it is that there is a strong prohibition against having leaven in your home, under your control, in your responsibility, or appearing to belong to you. So the discussion revolves around the edges of what does "your home" mean? What are the boundaries of taking ownership of or responsibility for (even if you don't own it, you're liable for it) a piece of property?

The Sages taught in a baraita: With regard to a gentile who enters the courtyard of a Jew with his dough in his hand, the Jew need not remove the leaven by evicting the gentile from his property. However, if the gentile deposited the leaven with him, and the Jew accepted responsibility, he must remove it. If he designated a room in his house for the gentile* to place his leavened food, he need not remove it… (h) (Steinsaltz Pesahim I, v6 p27)

There are a couple of footnotes on this:

(*) See Rashi and Tosafot, who disagree over the significance of this issue. The Rambam explains that according to Rashi, the assumption is that generally one who deposits an object with no stipulations expects the bailee to take responsibility for it. However if he designates a particular room for the deposit, that indicates that the bailee did not accept responsibility for it.

And

(h) …If the Jew designated a space for the gentile to leave his leaven, but the Jew did not take responsibility for it, the Jew is likewise not obligated to remove it. The halakha is in accordance with the opinions of Rashi, the Rif, and the Rambam, who maintain that the designation of a place exempts the Jew from the obligation to remove the leaven only if he did not acept responsibility for it… (footnote)

And:

Rav Ashi said: …If [the Jew] designated a room in his house for the gentile to place the leavened dough, he need not remove it, as it is stated: "It shall not be found in your houses," and that house is not his; since when the gentile brings the dough into the house, he brings it into his own house, as the space was designated for his use. (Steinsaltz Pesahim I, v6 p27)

(They then rule that other related rulings regarding renting to a gentile who might bring in idols to a space s/he rents from a Jew do not apply here.)

And finally a recommendation that in the case of a gentile who brings leaven into a rented room in a Jew's household, the leaven should be very clearly segregated and marked so it's not accidentally consumed.

And Rav Yehuda said that Rav said: If leavened bread belonging to a gentile is in a Jew's house, [the Jew] should erect a barrier ten handbreadths high around it on the fourteenth of Nisan, as a conspicuous marker, so that he will not mistakenly eat it. (Steinsaltz Pesahim I, v6 p28)

"Taking responsibility" would mean that if something happened, e.g. the house got broken into and the leaven was stolen, the Jew would be obligated to reimburse the gentile for the value of the leaven. I don't think this would be the understanding in a modern roommate situation (if your house gets broken into you wouldn't expect the landlord to make good on your losses and anyway that's not legally allowed perhaps except in a case of gross negligence i.e. the locks stop working and the landlord dallies in fixing them).

Anyway, the net net is that of course all this depends on which particular thread of Judaism your roommate practices. The most courteous would be for you to refrain from bringing leaven into the house during Passover (so she doesn't accidentally eat it, or have others think she is eating leaven). However, it does seem like it would not put your roommate in violation of halakha if you were to bring leaven into your own personal bedroom and keep it there during Passover.