Since Westeros is an island, the seas should continue around the north. Can ships move around the edge of the top of the map, between the Bay of Ice and the Shivering Sea?
There's no movement outside of the board, and no justification in the rules for these areas to be treated differently. The two sea regions you mention aren't adjacent to each other, nor are they the same region, so ships can't move between them.
As for the lore behind this, the Game of Thrones world is big, and not thoroughly explored. It's likely too dangerous or lengthy to sail around the North pole. The wiki says:
The maesters also understand that theoretically, a ship should be able to circumnavigate the globe, by continuing to sail west from Westeros until they come around to Yi Ti on the other side, then continue going west until they return to Westeros. They also understand that a ship could sail north over the pole and reach Yi Ti on the other side—provided that there is no landmass or arctic ice in the way. However, as of yet no ship has ever successfully circumnavigated the globe. Ships that have sailed west of Westeros and returned report finding only a vast ocean, and other ships simply never returned. Even the far south of Sothoryos and eastern end of Essos are unknown to men in Westeros. There have been some attempts to navigate north over the pole, but all have ended in failure due to dangerous ice and other unknown dangers.