Transporting Sheep in Minecraft
You probably would not need to take them home. You can dye your normal sheep by making dye and right-clicking the sheep while you are holding the dye in your hand. Alternatively, you have a few options:
Using a nether portal
When you hold wheat in your hands, cows, sheep, mooshrooms, and other animals (excluding pigs) will follow you. As of version 1.4, animals, mobs, etc. are able to go through a nether portal. Now, combining these two things together, you could hold wheat (or carrots for pigs) to make animals follow you through a nether portal. Now for the tricky math. Following the article here, one block traveled in the nether is equivalent to eight blocks traveled in the overworld. However, if you are too close to the original overworld portal, you will end up where you started instead of where you are supposed to be. You must travel at least 128 blocks away from where you started (in the nether, 1024 blocks in the overworld) in order to not have your nether portal link to your existing overworld portal.
Using a Minecart
You could build a minecart track from your main base to this island to allow for efficient travel. However, you would need to make a bridge for this, even though you can travel faster by Minecart. It would also be easier to transport the animals because you can shove them into the Minecart and push it.
Land Bridge
The least efficient way to transport them (in my opinion) would be to make a land bridge and hold some wheat in your hands. After that, they will follow you as you walk. However, if you switch to another item, they will stop following you. Therefore, make sure you eat some high calorie snacks before starting your journey :).
END NOTES: The best way to go would be to use wheat to guide your sheep or other animal into the Nether Portal. From there, make Minecart tracks to wherever your base is. Note that maps do not work in the Nether. If you are not in a position to do this, you could use a land bridge, but just know that it will be far less efficient.
You do not need a bridge. Sheep do not drown.
If you do not want to build a Nether path, just grab some wheat, a boat, and turn the TV on - it's gonna take quite some time. If you sail slow enough, sheep will keep up. Even if some of them lose you, just come back - they'll float!
Once upon a time my wife and I have led a herd of 8 mooshrooms over 8 kilometers this way - 6.5 by sea, 1.5 by land. It took like 4 hours - we took turns, like truck drivers :) We've only brought 3 to the end, but whatever - yay for infinite soup :)
You can dye a sheep with whatever color you like. First, you have to make the dye as described here. After you do that, right click on a white sheep while holding the dye in your hand.
Better late than never: Bring a boat and a lead. I read above and since sheep won't sink, I dragged a sheep across an ocean. I didn't try multiple sheep, but I'm sure that's possible.
I'm in 1.13.1 and did not row full speed, but had a great pace. I managed to not drop the lead. Not sure if lead dynamics have changed in the 4 years since I played, but I didn't want to have to swim to get a broken lead.