As mentioned previously, Birkat Hagomel must be recited in a Minyan and there are differing opinions as to whether or not the person reciting it counts as part of the ten or if there need to be at least ten men in addition to the person reciting it. Practically speaking, the one reciting Birkat Hagomel may be considered part of the Minyan and recite it as long as there are at least nine other men. Another facet of this blessing is that it is commonly recited in the presence of a Sefer Torah. The Nimukei Yosef, (Berachot 54) says that since the verse in Tehillim alludes to reciting the blessing before Torah scholars, the Torah is a fitting substitute to them. According to this opinion, one would not need to have an actual Aliyah to recite Birkat Hagomel. Rabbi Aharon HaLevi and other Rishonim state that another reason is that it is preferable to recite the blessing with an Aliyah to the Torah is that just as one is performing a Mitzvah by going up to the Torah, one should follow it up with another Mitzvah, namely, Birkat Hagomel. It should be noted that, although it is preferable to have an Aliyah, or at least the presence of the Sefer Torah, when reciting BirkatHagomel, it is not an obligation. Indeed, the Biur Halacha (§134) says that one is not permitted to take an Aliyah from someone who has a Yahrtzeit or a Bar Mitzvah so that one could recite Birkat Hagomel.
The Shulhan Aruch (Orah Haim 219:6) says that one may recite BirkatHagomel at any time after one traveled, left the hospital etc., but that it is proper to recite it within three days of the event. Some opinions suggest that there is a possibility of reciting a blessing in vain if it is recited after three days, but the Halacha follows the Shulhan Aruch. This has been confirmed by Rabbi Mordechai Eliyahu. One explanation is that Birkat Hagomel is analogous to the Korban Toda, which does not have a time limit.
Summary: Although Birkat Hagomel it is preferably recited when one has an Aliyah, or at least when the Sefer Torah is taken out, this is not an obligation. One should preferably recite Birkat Hagomel within three days of travelling, but may do so any time after that.