The bank are just after the investment of your money OP because you must have some- they've not invited you as a status thing, they'll have done it to a large number of account holders- it's part of their job to secure additional uptake of their services. Like upselling in a shop really, they have targets, I expect they're surprised you agreed to it!
I don't think 'the bank manager' is really seen as anything impressive or a status job these days such as it was back in the day, she or he is just a normal person like in any other shop basically, Which is what I assume people here are getting at but could've been gentler about.
I would not consider dressing up for the bank manager in a million years, or even going in to be honest to hear a sales pitch about how the bank can 'help' manage my money. If you want impartial financial advice OP I would recommend speaking with an independent financial advisor if you want to be more involved with your money and direct where it is invested appropriately. Since it seems like all you want to do is something that can be done online, why even go? Get a banking app on your phoneand sort it in 5 mins and save the stress I say!
I think it unusual you're concerned about embarrassing your husband OP, and want to stress smartly to represent him well outside the house. You don't work for him and I would bloody hope he is proud of you at all times, empowers you as an equal partner to him and doesn't place old fashioned expectations on you such as these 
. Your husbands just a person at the end of the day, unless he's the royal family I doubt most other people give a fig about him and his local prowess, nor would they dress up to meet him- it's not the 1950's -ditto the bank manager, they aren't your superiors and do not warrant such adjustment nor do you need to impress them. These days even if he were the RF most people wouldn't be fussed, I know I wouldn't. They're not our betters.
It seems a shame to be viewing a very normal meeting as opportunity to husband please and cause yourself worry- You're just as important OP, and I'm not actually sure the bank 'meeting' is even what you think it is, it's just a sales pitch most people would regard as a spam invite which they would decline.
Your DH may well be a lovely person but you sound in awe of him. At the end of the day he's doing a job he gets paid for, he's not a saint out changing the world for our children Especially if he's involved in local politics, say. We all try our best at work and have good intentions for society, it's what decent normal people do as standard and doesn't require such fawning.
You are right though that you are not at fault here though and don't deserve to feel bad or be mocked. But you are sounding a bit over the top OP and it would benefit you to realise it. You don't need to try and guilt people with the martyring either.
With regards to clothing I really think anything smart-ish would be more than fine. M&S for trousers perhaps if you would prefer them to jeans? The bank know you have money or they'd not have invited you, there is no impressing you need to do in that regard. Though with that said, they invite me often enough and I don't have a great deal, it's on the same level as a nuisance telemarketer call for me.