I know this is going to be a hard one. I only have one day and I want to see both Bruges and Flanders Field. Is it possible to do 1/2 and 1/2? And how to do it? A private guide? Or if not, I would put Bruges first and spend the whole day there. Any thoughts? I am actually on a river cruise and docked there for the day. No car.
If it were me, and I could only visit one then I'd put Ieper/Ypres first and Brugge a distant second. As you suspect, I don't see how you can do both without rather short-changing them both. I suppose, if you've got a car and were willing to make a long day of it, you could quickly see Brugge in the morning then drive to the salient to tour a little of that area and end in Ieper for the Menin Gate ceremony. But it would be rushed - and, also, where do you begin and end, I'm assuming from a third town?
Are you starting from a hotel in Bruges, or starting in another city? Do you plan to have a car? What time of the year? What is your next stop? Will you have your luggage with you? How many of the churches and museums in Bruges are on your list?
The poem In Flanders Field was written during the long campaign in the Ypres area. The title does not, to my knowledge, identify a specific battle. However a museum in Ypres carries its name, as Wikipedia explains:
When my wife and I did the Quasimodo Flanders Field tour, it was a full day (0800-1700). Without a car, I don’t see how you could do both, and with a car, you’d be rushing both.