Rosemary thought there were six ways, but didn't send any of them in! Sarah and Claire sent in two possible maps, although they were both the same if you pushed them and pulled them a little.
Thank you to Allison's student at Stamford American International School in Singapore for this solution. The maps look different, but, like Sarah and Claire's solutions, many of them are actually the same. I can only find four distinct maps here, and one of them isn't allowed.
To help see how these solutions are the same, the diagram below shows the same maps as above, but with the positions of the islands fixed. This is because the map isn't really different if the island with one bridge coming from it is on the left, on the right, at the top, or at the bottom. Can you see how the maps are the same as the ones above, from Allison's student?
Can you find any more possibilities? The total number is more than 6, but less than 15!