One of my bridesmaids was due 3 weeks before my wedding - although she had a planned section so we knew when baby would come. Even if they induce you at term (is that the plan?), it can take a few days.
It worked really well for us as it happens, but as the bride I knew she might not be able to come and she was under no pressure to do so.
I think whether it is doable depends on how flexible the bride is willing to be. Will she understand if you have a horrible birth and are in no state to travel? I could barely walk 3 weeks after giving birth. Hopefully you’ll recover quickly, lots of women do, but you don’t know this.
Getting there is one thing, but also I would ask her what is expected of you on the day. I said to mine that if she didn’t need to do anything. If she could walk down the aisle, great, but if baby needed a feed then she could sit it out. Likewise photos etc, if she could then great but she didn’t need to. As it happens she did everything, but it really does depend on baby.
Does she want you to get ready with her in the morning? Can you take baby to that? You don’t know how you’ll feel about even a few hours away from baby. I know your husband is capable of looking after him or her but have a think about if you’re comfortable.
What is the bridesmaid dress like? I got a 2 birds one for mine so it is one size and can be done in a way with easy access to boobs (I know you’re bottle feeding but if you’re leaking or something). You don’t know what size you will be or want the Pressure of fitting into a corset dress!
Will the bride be expecting you to stay late? You may well be absolutely knackered and want to go home after the meal. Also if there a band or DJ in the evening, it might be too loud for baby.
Is there a quiet room at the venue you or your husband can go to with baby if they get fractious?
Are you comfortable if lots of people want to hold the baby? A sling can help deter people from wanting cuddles.
My advice would be you can aim to go but you can’t commit to go as there are too many unknowns. Her wedding is no less important to her because of your lovely news, so I think the main thing is don’t mess her around (I’m sure you wouldn’t), and be realistic. You sound like you really want to make the effort to be there which is fantastic, but 3 weeks post partum you do have to think of yourself.
Most importantly, congratulations on the pregnancy 