I have attended services in a number of different Ashkenazic synagogues on Sukos and Sh'mini Atzeres/Simchas Tora. When going around the bima for hosha'nos on Sukos, and, in most cases, when doing so for hakafos on Sh'mini Atzeres/Simchas Tora, people went counterclockwise (when viewed from above). Why counterclockwise?
Mishna Berura 660:1:3 says that when the Sefer Torah is on the Bimah those on the Mizrach (eastern wall) turn around to face the Torah their right side is now facing Tzafon (north) therfore they start in that direction.
Everything done in a Beit Kenesset is modeled on the procedures as they were done in the Temple, "HaMikdash", in Jerusalem. That is why a synagogue is known as "Mikdash Me'at", a small Temple (Yechezkel 11:16, Megillah 29a in the name of Rabbi Yitzchok).
In the Temple, when the first Kohen would enter in the morning to unlock the doors, they would turn to the right and proceed to go counter-clockwise around to unlock everything. All of this is based on the concept that the right side, "Kav HaYamin", is considered the side of kindness, "chesed".
Going to the left side, "Kav HaSmole" and proceeding clockwise is associated with judgement, "Din". This is the same reason why when ascending to the Torah for an aliyah, you approach from the right normally and depart from the left, counterclockwise motion. When someone approaches for an aliyah from the left, it is an indication that they are a mourner.
During Sukkot and on Hoshannah Rabbah in particular, we are drawing "Chesed" into the world through our avodah. That is the main idea behind the judgement pertaining to water that takes place at that time and the idea of "Simchat Beit HaSho'evah", the joy of drawing water from the wellspring. We are sweetening the judgements that are finally sealed and sent for execution on Hoshannah Rabbah. And therefore, we go to the right and counterclockwise.
We always do things from left to right as the right is superior in the Torah. As a matter of fact where I daven (pray) we are also makpid (מקפיד) to do boi besholem (באו בשלום) in lecho dodi (לכה דודי) counter clockwise.