Did the Old Forest go all the way to the East Road ?
 

Did the Old Forest stretch all the way to the East Road ? The reason I ask is that I've never seen a really detailed map of Buckland and if there was a stretch of the Hedge between the Brandywine Bridge/North Gate and the end of the Old Forest that was "bare", i.e. not adjacent to trees, why the Bucklanders bothered building that stretch.

The hedge wasn't planted as a protection against the Old Forest but against any threat from the East.

When the Hobbits first moved into The Shire, they had the river Brandywine as a protective barrier against attack from the East. The Hobbits who settled in Buckland lost that protection and so grew the Hedge.

The problems with the trees of the Old Forest came later.
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If you dig into the 2nd Age tales, much of the west of Middle Earth was forested, and was a source of timber for the Numenoreans to build their mighty ships.

It doesn't appear so. There is a map of the Shire online that shows Buckland (here) and the northern border of the Old Forest doesn't appear to border the East Road to Bree.

Elrond, and later Treebeard say that Fangorn and the Old Forest come from the same ancient roots - that there was one big forest with the future Old Forest on it's north west side and Fangorn on its east.
I'm guessing that it did stretch to the East Road.