I know that are not allowed to make money or do business on Shabbos. What do I do about my air B&B when I rent it out to Jewish families over Shabbos am I not allowed to charge them for their stay on Shabbos?
There is no issue with renting out a property for the duration of Shabbos, whether to Jewish or Gentile guests, so long as their stay in the property will begin sometime before Shabbos. Furthermore, even if they will only be staying there on Shabbos itself, if the payment for the Shabbos stay will also go towards covering the work that the owners need to invest in cleaning and preparing the property before and after Shabbos, then it is also permitted.
It is indeed correct that it is forbidden for one to earn money for work that one does on Shabbos and the Poskim rule that this prohibition also applies against earning money from a rental and job. This prohibition is known as Sechar Shabbos. However, this prohibition only applies when one is being paid individually on its own just for the Shabbos work. If however the payment includes also payment for work that one did before or after Shabbos, then the sages permitted to have once Shabbos wages included within that payment, so long as one is not being paid a specific sum for the Shabbos work alone, but is rather being paid collectively for all the work which also happens to include the work on Shabbos. This concept is known as Havlah. Accordingly, there is no issue with charging rent for guests who will be staying on one’s property over Shabbos, as common practice by short-term rentals is to give them access to the property starting from the early afternoon, and hence it ends up that the rental price that they will be paying includes payment for using the property when it is not yet Shabbos. Likewise, they also will be staying in the rental for some time after Shabbos. Accordingly, the rental payment that they will be charged for Shabbos is mixed with weekday payment and is a true definition of Havlah which the sages permitted to be earned. If, however, one is renting it per hour on Shabbos, such as for Shabbos afternoon, or the guests will only be given access starting Friday night and leave the next morning, then seemingly it would be forbidden for the owner to charge the money for this day, due to the prohibition of Sechar Shabbos. On the other hand, perhaps one can argue that since part of the payment is going towards cleaning and arranging the room in preparation for their stay, and after they leave, which will undoubtedly take place before and after Shabbos, therefore it ends up that here too the money earned for their Shabbos only stay, includes payment for work that was done by the owner during the weekday, and is hence once again defined as Havlah. Likewise, some of the payment goes towards paying water and electricity bills, which is not considered actual profit but simply paying expenses, and since this too is included within the rental price it is therefore considered Havlah. Furthermore, some Poskim argue that since having Jewish guests is a mitzvah of Hachansas Orchim, it is therefore permitted to earn money from their stay being that it is considered for the sake of the mitzvah. [To note however that this approach is not unanimous amongst the Poskim.] A further allowance recorded in the Poskim is to already collect payment for the rent prior to Shabbos, and thereby have the property be considered as purchased by them over Shabbos.
Sources: See regarding the prohibition of earning money from renting out a room for Shabbos: Admur 306:9; M”A 306:7; M”B 306:11; Ketzos Hashulchan 107:15 footnote 25 See regarding the allowance today to rent out a room for Shabbos due to it being considered Havlah: Halef Lecha Shlomo 125; Or Letziyon 2:25;-1; Teshuvos Vehanhagos 2:197; SSH”K 28 footnote 143 Piskeiy Teshuvos 306:11 See regarding the allowance to rent out a room for Shabbos due to it being considered Tzorech Mitzvah of Hachnasas Orchim: Mahrsham in Orchos Chaim 306:4; Nefesh Chaya 307:5; Minchas Shabbos Mincha Chadasha 90:8; Ketzos Hashulchan 107 footnote 25; Divrei Moshe O.C. 9; Devar Yisrael 1:99; Teshuvos Vehanhagos 2:197; Piskeiy Teshuvos 306 footnote 72; See Pesachim 112b and Bava Metzia 85b See regarding the allowance to rent out if collect payment before Shabbos: Maharshag 2:60;; Ateres Moshe O.C. 55; Piskeiy Teshuvos 306 footnote 72 See general sources regarding the prohibition of Sechar Shabbos and the allowance of Havlah: Admur 243:5 and 11-12; 244:15; 245:2; 246:1 and 13-15; 306:8-9 and 11; 334:7; 526:14; 585:11; Mahadurah Basra on Chapter 243; Michaber and Tur 246:1; 306:4-5; Rama 246:2 and 306:4; M”A 243:1; 246:3; 306:7; Bava Metzia 58a; Rambam Shabbos 6:25; Tosafos Shabbos 19a; Mordechai Shabbos 246; Rosh Shabbos ibid and 23:8; Rabbeinu Yerucham 12:12; Sefer Hateruma 221; Semag L.S. 65; Shibulei Haleket 113; Beis Yosef 243; Tzemach tzedek O.C. 49:3; Alef Hamagen 585:24; M”B 306:21; Piskeiy Teshuvos 306:6-9 and footnote 66; See regarding if Sechar Shabbos is permitted for the sake of a Mitzvah: Yes: Second opinion in Admur in 306:11 and the final custom mentioned there; 2nd opinion in Tur 585 and Michaber 306:5 and implication of Michaber 585:5; M”A 585:12; Elya Raba 585:17; Beis Meir; Kaf Hachaim 585:49; No: Admur 585:11; First opinion in Admur 306:11; Tur 585 in name of Rav Yechiel and Mordechai; first opinion in Michaber 306:5