DE1-SoC Transferring data from the FPGA to the HPS

You have a number of choices. Depending on what tradeoffs you want to make between performance, engineering design time, and FPGA resource usage. You could use the HPS to FPGA bridge and use the HPS DMA engine to transfer data. You could also include a DMA engine in the FPGA fabric and connect to either the FPGA to HPS bridge or the FPGA to SDRAM controller bridge. If you don't need to move lots of data or don't care about performacne the simplest way would be to use the H2F bridge you have setup already and do read operations instead of write.