I was armed with the M14 in 1963-66 and usually volunteered to be the guy with the selector switch and bipod. (This was before the E2 was widely issued - never saw one in service.)

I can vouch from experience that the bipod was mounted so as to fold forward for carrying. It was a substantial, lumpy assemblage of hard steel that would have been uncomfortable either at sling arms or shoulder arms had it been folded back over the forearm.