Yes you are right that Billy Jack was probably the first chance for some of us to see some Hapkido, but nowadays it is hard to find anyone under 50 who has heard of that movie. Now Bruce Lee with Doju Ji Han Jae everyone has seen.
But because of BJ, a whole generation was introduced to Hapkido. As a result, interest in the art here in the west took off by leaps and bounds. One instance in which Hollywood did something positive.
In regards to Bruce Lee and Ji Han Jae, I'm assuming you're talking about 'Game of Death'? Unfortunately, this movie was mangled after the passing of Lee. A lot of footage surfaced later fortunately. However, Jae did not represent Hapkido in that film. He was actually portrayed as a Chin Na master according to the screen play and the vision of Bruce Lee. Hapkido was represented by one of the guys that were with Lee and was continually getting his butt kicked. In fact, Jae as the Chin Na master thoroughly defeated the Hapkido master. So anyone outside of the art of Hapkido would probably not know what role Ji played in Hapkido from this movie. In fact, if anything they'd think his art was Chin Na.