This is the secret to fitting writing in: Write in your spare moments, especially if you have “spare” moments that occur the same time every day — a smoke break, lunch, etc. Some folks even write during their 2-5 mins in the restroom each day (I don’t do this, and nor do I particularly recommend it — this is just an example of how far you can go).
Make space for writing in your life, and keep going to that space every day. Joseph Campbell called this your “sacred space”. I use it for writing, but he meant it to be your personal time for anything — your withdrawing from the world time, where the world cannot touch you.
He also said that at first it may not seem like much is happening, but if you build your sacred space — and you keep going there — eventually something will happen. You will find your center, and from there, your bliss.
In my opinion, if writing is your bliss, you will write.