Haha well it was your first experience and we were cheesing the entire HM run since all of us are Level 31s plus we're a 5 man team. We're sorry that you couldnt experience the raid the legit way so the next time when we're doing it on NM run we will definitely teach you on how to do this correctly.
As for the reasoning why the hunter (which is you) should cross over the bridge is due to 2 reasons:
1. Hunter can go invi so should in any emergency situation arises during that time you can just blink strike invi and run off to safety.
2. Our method that time was to cheese the bridge part which requires warlocks sunsinger to do with the revive ability to clear/erase the mobs from our side.
For reason no.2, to better understand why we're doing this, let me explain on how this part actually works. In the legit way, there are 2 phases, the 1st phase is for each guardian to kill off the sword bearer which will then cross over to the other side and kill the Gatekeeper. The gatekeeper is invulnerable to all attacks except the sword (hence why we need to kill the sword earer), once each guardian has cross over the bridge and after each slaying the gatekeepers slain, then only the 2nd phase of this section would kick in, and that would be to kill off all mobs. Once that is done this bridge section is done.
Now the requirement is to have at least 1 guardian on the other side to have the system register that the fireteam has crossed the bridge. Once that is done, when all guardians at the beginning side of the bridge dies, it would register into the system that all remaining guardians have crossed the bridge hence proceeding the system to go into the 2nd phase. Warlocks will then revive at the beginning area that would then snipe from there to clear the mobs on the your side safely. Once all mobs are clear (except the gatekeeper), the section is considered clear.
If anyone feels that my explanation is off, please do correct me

Also for Reason 1 is not really valid, any guardian can be on the other side, its just that on our 5 man team you're the only hunter and the rest of us are warlocks whom can revive.
It is way harder to do than said. First you need 3 person to form the bridge (2 on each totem, 1 in the middle). The more people you send to the other side of the bridge, the harder for the remaining guardians to bring down swordbearer
forming the bridge. The fun part begin when you have 3 guardians on each side of the bridge....
The 3 guardians that crossed over to the other side need to form the bridge for the remaining guardians to cross over. This time will have wizard/knight/gatekeeper(if not dead) and still need to hold 2 totem + forming the bridge