Bistatic backscatter communication (BackCom) allows passive tags to transmit over extended ranges, but at the cost of having carrier emitters either transmitting at high powers or being deployed very close to tags. In this paper, we examine how the presence of an intelligent reflecting surface (IRS) could benefit the bistatic BackCom system. We study the transmit power minimization problem at the carrier emitter, where its transmit beamforming vector is jointly optimized with the IRS phase shifts, whilst guaranteeing a required BackCom performance. A unique feature in this system setup is the multiple IRS reflections experienced by signals traveling from the carrier emitter to the reader, which renders the optimization problem highly nonconvex. Therefore, we propose algorithms based on the minorization-maximization and alternating optimization techniques to obtain approximate solutions for the joint design. We also propose low-complexity algorithms based on successive optimization of individual phase shifts. Our results reveal considerable transmit power savings in both single-tag and multi-tag systems, even with moderate IRS sizes, which may be translated to significant range improvements using the original transmit power or a reduction of the reliance of tags on carrier emitters located at close range.