Best thing is put your four ways on when approaching your entrance. That way the people behind you at least have a clue that your about to do something out of the ordinary. Wait for a sizeable break in oncoming traffic and begin your maneuver. Try to keep the gap in your lane small so as not to give the impression that the cars behind you should sneak by you. Although sometimes that's inevitable. Then just remember take your time and do what you need to do in order to make a safe back. People will probably get angry but try your best to ignore it.
This is one place I used to go regularly that it was easier to blind side and dam near impossible sight side back. So i would come over the bridge and block traffic then wait for the oncoming light to turn red and make a break for it. Sometimes you just get those situations where you just gotta do what you gotta do.
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You should in my opinion attempt to wait for a gap if at all possible or get someone to help stop traffic for you (like a codriver or employee of your consignee. At Coca-Cola in downtown Atlanta, security there blocks the street so you can get into their "tower dock" which requires a blindside back (using the whole street) to back down a tunnel which continues to curve on the blind side to reach an underground dock.
Consignee:
The customer the freight is being delivered to. Also referred to as "the receiver". The shipper is the customer that is shipping the goods, the consignee is the customer receiving the goods.