The bid construction problem (BCP) for combinatorial total truckload transportation service procurement auctions consists of determining one or several bids and the ask price for each bid, where a bid is defined by a subset of shipping contracts. In this paper, we consider novel variants of the BCP which include business side constraints, namely, upper limits on the total number of contracts covered by the generated bids and on the number of contracts included in each bid. To solve the BCP variants, we propose a branch-price-and-cut algorithm which is based on techniques that have proven their efficiency on classic vehicle routing problems, and test it on generated BCP instances. Our computational results show that the proposed algorithm identifies optimal solutions within reasonable computing times for the different variants of the BCP, with and without business side constraints. Regarding bids quality, we observe that adding these side constraints may be more or less beneficial for a carrier, depending on its size, and on the values given to the parameters defining these constraints.