Q. Can we invite on Shabbat someone who would be traveling if our intention is to do Kiruv, don’t we always say “desecrate one Shabbat so he can keep many?

A. Indeed the Talmud (Yuma 85a,b) mentions in the name of Rabbi Shimon Ben Menasio that rationale as one of the basis for defiling Shabbos to save someone’s life. The Talmud there mentions other sources for this ruling too, the one that is chosen as preferred is Shmuel’s reason: “You shall live by them – and not die by them” (Vaikro 18:5) which does not apply in your case. Whether Rabbi Shimon’s grounds remain viable is subject to dispute in the Poiskim. Moreover, his reason is also subject to a limitation, it does not apply in a case of doubt, as the Talmud explains. Inviting someone for Shabbos is not a guarantee that it will lead to actual Kiruv.

In addition to the above, Mishna Berura (306:57) on the Shulchan Oruch’s case of a captured daughter that is about to be converted, quotes the Poiskim’s ruling that desecrating Shabbos in order to save her applies only if she is not at fault. Otherwise we would rather rule “We don’t tell a person to sin in order to provide merit for someone else”. Whether this applies in your case, depends on the actual circumstances. Mishna Berura, does quote Rabbi Shimon’s reason in regards to saving a minor. (Magen Avraham ibid.)

In practice, Poiskim differ. Many rule that it is not permitted to invite someone who we know will be desecrating Shabbos in order to attend. (Igrois Moishe O.C. 1:99 and 98, Shevet Halevy 8:146, Tzitz Eliezer 6:3 et al.).
However, Teshuvos Vehanhogos (1:358) Bein Ysroel Loamin (13) and Yashiv Ytzchak (O.C. 11) are of the opinion that when the objective is Kiruv, there is also a sincere intent of explaining during that Shabbos the importance and holiness of the day and the parking of the vehicle is not immediate to the house, it is permitted.

Horav Shlomo Miller’s Shlit”a opinion is that, since each case has its own merits and variables a competent rabbinical authority should be consulted on every occasion.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a

Please refer also to the prior question #207, on Inviting to a Simcha a relative who would travel by car on Shabbos.