On the Sch C ... YOU have barter income and then a rent expense deduction ... that is the proper way to report this exchange of services.
And they should give you a 1099-b for the barter income box 13 : https://www.irs.gov/pub/irs-pdf/f1099b.pdf
And you should give them a 1099-misc for the rent paid box 1 : https://www.irs.gov/pub/irs-pdf/f1099msc.pdf
