Using a storage interface circuit of a programmable IC, a first set of configuration data can be communicated between a storage circuit and the programmable IC. Using the first set of configuration data, the programmable IC can be programmed to include: a bus interface module that is designed to interface with a host device over a communication bus that links multiple devices, and an internal configuration access interface that is designed to interface between the bus interface module and programmable logic of the programmable IC. Using direct memory access (DMA) transfers through the bus interface module, a second set of configuration data can be communicated between a memory circuit and the programmable IC. Using the second set of configuration data, the programmable logic of the programmable IC can be programmed.