Oddly enough, I was only asked twice in 18 months of presenting female about the mismatch between my presentation and my ID. And I have done a lot of traveling, including several international trips. Having an ID matching your gender is very affirming, so I would opt for it. As long as the picture is close to your appearance, I don't think it would be a big deal. Also, keep in mind, there are many masculine looking cis women.
It may help in the bathroom situation if anyone ever asks, at least you can show a female ID. The big issue is that in the US laws are different by state. If I drive 15 miles, I can legally use the bathroom of my choice as a transgender person. In the state I live in... not so sure.
I have to admit that the first 7 or so months of being fulltime, I did figure out ways to avoid the bathroom dilemma. By then I passed well enough that I used the ladies room and never had an issue but who knows. In the early phase, my mantra was: If I present 100% female, it would be the ladies room, if there could have been doubt (e.g. just wearing jeans and sneakers) it was the men's room, even though I did get questioned about that several times.
So, my recommendation would be to get your new ID! The bathroom you can always decide on a case by case basis.
Hugs, Sarah