I know it is forbidden to leave Israel. When Bibi and his government (or any administration) go on political trips, say to DC, how is this not a violation of the mitzvah?

ב"ה ב"ה Shalom I will not expand upon travelling abroad in general, but I will focus on your specific question. The prohibition of leaving Eretz Yisrael, is not an airtight prohibition without exceptions. The prohibition is mainly that a person not permanently reside outside Eretz Yisrael. The Rambam (Hilchot Melachim 5: 9) enumerates a few circumstances allowing a person to leave Eretz Yisrael temporarily. 1. To study Torah. 2. To marry 3. To saves people or things from idol worshippers 4. For business. Tosafot (Avoda Zara 13a) expand this permission to allow leaving Eretz Yisrael for other Mitzvot as well. Rav Eliezer Valdenberg zt"l ()Tzitz Eliezer Vol. 10, 46:2) that people rely on this Tosafot to allow exiting Eretz Yisrael for other Mitzvot as well. It follows that when a government official leaves Eretz Yisrael, since the official is serving the political, security, economic or other interests of Israel , the person is going to fulfill a mitzvah for the sake of the Jewish people, it is allowed to leave Eretz Yisrael. All the best