My aortic root is mildly dilated like yours, and my ascending aorta was where the aneurysm was occuring. I had an ascending aortic measurement of 4.5 for about 10 years, and was under a watch. In the last year it (ascending aorta, not the root) went from 4.5 to 5.4, so I went in for surgery. They replaced the BAV at the same time even though by itself it wouldn't have required the surgery yet. It was better to get them both now rather than wait and have a guaranteed second surgery.
My particular surgeon said that 5cm was her point for recommending surgery, although I have seen recent references saying that for folks with BAV they are thinking that 4.5cm is a better target. The correlation of connective tissue disorder and BAV was cited as a reason to possibly move this recommendation downward. I think there is no hard and fast rule for when to repair or replace, and that it may depend on the surgeon and the patient's other circumstances, but if I were in your shoes I would be asking about a graft for the ascending aorta. I think at 3.7cm diameter in the root (may want to confirm this with a CT) you are only considered on the high side of normal, so they may not recommend replacement of that. But again, this is something to discuss with your surgeon's team, definitely.