The Shulchan Aruch[1] rules that one should not take a sefer Torah to a prison in order to read for the inmates, who otherwise would not have access to kri’at haTorah.[2] The Mishna Berura[3] explains that it is a zilzul (degradation) of the sefer Torah to be taken to people, even to those who need it, as they are supposed to congregate around it in its place, not the other way around. Some poskim[4] say that zilzul applies only when those in need can make it to the sefer Torah (as opposed to inmates). However, the Shulchan Aruch’s ruling is generally accepted.[5] Moreover, in your case, it is likely that the great majority of the minyan’s participants do have other opportunities to hear kri’at haTorah other than on the train. Thus, we have to explore if there are other grounds for leniency.
The Yerushalmi[6] says that it was permitted to bring a sefer Torah to the kohen gadol because of his stature, and the Rama[7] extends this principle to other “important people.” The Bi’ur Halacha[8] states that if there are ten inmates, then the Shulchan Aruch would agree that their obligation to hear the Torah reading makes it proper to bring the sefer Torah to them. The Nishmat Avraham[9] cites Rav S.Z. Auerbach as saying that a “community of ten” probably has the stature of an important person. However, both refer to situations in which the ten men would have no way of hearing kri’at haTorah if the Torah is not brought to them, which, as noted above, is not likely in your scenario.
Some poskim discuss the idea of bringing an aron kodesh along so that the sefer Torah is shown respect and has some permanence in its temporary location. This idea is rooted in a teshuva of the Maharam Padova,[10] but he also mentions an additional mitigating factor – that the sefer Torah will stay in that location for at least a day or two.[11] (The Kaf HaChayim[12] says that using an aron is enough according to the lenient opinion). We understand that in your case, the sefer Torah is brought in and out with a passenger on his commute.[13]
A more convincing leniency takes into consideration the context of the use of a particular sefer Torah. The issue of zilzul is more pertinent if a sefer Torah that is based in a shul and is used there for public reading is moved temporarily for the needs of an individual. However, it is entirely acceptable to write a sefer Torah for the specific purpose of the owner taking it along with him to learn from in various locations. (In fact, this is the way the mitzva to write a sefer Torah was apparently intended,[14] and this is what was expected from a Jewish king.[15]) The gemara[16] relates that after the Yom Kippur service in the Beit HaMikdash, many people would bring their own sifrei Torah to show how nice they were. Some poskim[17] deduce from this anecdote that a personal sefer Torah does not have a restriction on its being moved. Logically (and this view has backing in the language of some sources), the issue is not so much the ownership per se as for what purpose the sefer Torah is intended. Moving a privately owned sefer Torah that has been used repeatedly in one place might be problematic. In contrast, it might be permitted to move one that was made in order to be utilized in a roving manner,[18] or even to designate for this purpose a publicly owned sefer Torah that is no longer being used in shul.
It is likely that some of the classical poskim who do not discuss this relatively new distinction do not agree with it. However, leniency on this matter is certainly legitimate, and we have seen a teshuva of Rav David Spektor[19] in which he permits it. Therefore, this issue should not be grounds for qualms about joining this minyan. (A separate discussion is required regarding the advantages and disadvantages of davening in this unique setting.)