A bride who doesn't understand that an ebf baby can't be left all day is a bit of a 'zilla tbh. Why should your son have to get used to a teat (and go through the associated upset and hassle) just to accommodate her?
But could you not equally argue: A guest who doesn't understand that the bride doesn't want her day potentially ruined by crying babies and screaming toddlers is a bit of a PFB tbh. Why should she have to adapt her day just to accommodate someone who hasn't quite thought through the logistics of childcare for a breastfed baby and should perhaps have got him used to taking a regular bottle knowing that she'd have to leave him for the day?
(OP I am not saying that you are being PFB by the way, or that you haven't thought things through. Just playing devil's advocate slightly, and suggesting another way of looking at the situation).
But I do think people get a bit hung up in general about BF babies and weddings. And that is speaking both as a bride who ten years ago said 'no babies/children' at her own wedding (and never regretted it, or felt the need to apologise once I became a mum), and now as a mother of three, who has breastfed them all, and occasionally had to miss out on social gatherings excluding babies and children as a result. I do think it would be unfair of you to expect the bride to let you bring him (unless you are family, which is slightly different); the problem is, if she lets you bring him, she has to let others bring their babies, and that's probably not possible to accommodate. I have never been to a wedding with babies/children allowed which hasn't been interrupted or spoiled by them in some way, and as a result I don't think it's in the slightest unreasonable for couples to have a blanket ban on children at their wedding even if that includes very young BF babies.
I think you either need to
(a) invest a bit of time over the next few weeks getting your LO used to settling without you every so often (a few trial runs of leaving him, as others have suggested, or getting into a routine of DH offering an evening bottle three or four nights a week to get DS used to it), or
(b) explain to the bride that unfortunately you won't be able to make it as you are breastfeeding and no-one else can settle DS to sleep and you would find it too traumatic to leave him, or
(c) do a kind of halfway house - go to the wedding, then do the 45 minute drive home to feed/settle DS, then return for the evening reception. Or just do the wedding itself and skip the reception - I've done this myself when DS1 was 3 weeks, left him with my mum for the hour of the wedding ceremony and then went home leaving DH to attend the reception on his own.
I hope you can find a solution that you are all happy with, and that if you do go to the wedding, you have a lovely time!