There are a lot of good answers here, but i wanted to answer from the other side of the fence. I know my situation is not exactly the same as the OPs but i thought it might offer a small amount of useful insight into how Bob feels in this situation
I was raised in a similar way to Bob, that the gentlemanly thing to do is to drive and pay for dinner/drinks when out with a woman. now this extends to both my girlfriend and to other woman on the very rare occasions i go out with a colleague or an old friend without my GF. now this is an ingrained behavior; i appreciate it is not in keeping with Feminism or equality standard of today, however it is still something that i feel strongly about, as i said its how is was raised.
For a moment we'll ignore my GF and come back to her later. i'll start with a couple of female friends, I know that they are independent women and like to make their own way, but when they pay i feel i'm letting them down. I KNOW this is not the case but it is still the way i feel. and that uneasy feeling those few women may have which as similar to those feelings of the OP are probably about equal to the uneasy feelings I have when they pay. there is no romantic intentions between myself and these other women but the gentlemanly feelings are still there.
Most of the time my friends know its just how i am, and agree to let me pay for the meal, however if we go out of an evening to the pub, they will always push past nad pay for drinks before i get a chance to get to the bar, this frustrates me but they've informed me that if i'm not going to let them pay for lunch then they're buying rounds!!!
This simple friendly almost jovial but firm stance left me with two choices:
- Ignore them and demand to pay, which in itself went against my gentlemanly mindset as ignoring them or going against their firm wishes is outright rude
- suck it up and let it happen
I know this makes me sound bad, but after some time and many occasions like this when the women suggested grabbing lunch, we went and when it came to paying they would say "No, i'm paying my half" i would allow them to do so. they always did this politely and without anger in their voices but were firm about it.
The thing is i'm still uneasy each and every time it happens, if Bob was raised in a similar many to myself then he will never be happy with the situation so ingrained is this mentality, but he may be willing to accept it
Yes i know this is not the same situation as its between partners in a Romantic relationship but... the methods she has taken to break my habits in this regard may be of use. my GF is a fiercely independent woman, but due to an eyesight problem is unable to drive, so we'll ignore driving from this.
Myself and my GF often go out for lunch or dinner, (rarely anything posh its usually just pub grub) when we first started dating this actually caused some friction between us as she wanted to pay for dinner or at least half of it and i wanted to pay in full. so she began a campaign to break my gentlemanly habits, it began with:
- If i left the table to use the facilities or go for a cigarette (Yes i'm a smoker, yes i know its unhealthy) she would get the bill while i was away from the table.
- She would suggest going out for dinner but only under the condition
that she be allowed to pay
- She would book activities which could be paid for in advance and then any difference at the end i was "allowed" to cover
These days if my GF says she's paying then i no longer argue, i don't try to pay behind her back, I accept its her choice despite how uneasy it makes me feel.
If she leaves it open however then i'm going to pay!
Opening Car Doors
This is the exception to the rule. opening or holding open a door for someone is something i will always do if able to do so, and quite frankly i will not stop it, its only meant as a polite gesture. i will admit i don't go running around to the other side of the car as quickly as i can though. if they get the door open before i can, then i can't exactly stop it can i?
Edit as per a comment:
I'm not suggesting you or anyone should feel sympathy for Bob, although i understand how this answer might read that way. Just that the automatic assumption that Bob is definitely acting this way because has romantic intentions is incorrect. its possible of course but it could be something else and may explain they way he acts which are not always obvious.
I was further detailing my feelings to explain why my missus and others had to use the methods they did in order to "break my habits" I knew i didn't need to do those things but "i was just being nice so why was anyone getting annoyed" was very much MY mindset until proved otherwise.
I appreciate this final section will likely attract downvotes but: For the OPs sake i hope they can convince bob to calm his conduct without causing offence or embarrassment to either party, but if Bob is truly just being a gentlemen without other motives as the OP suggested is possible, then i hope they can find a middle ground where neither feels uneasy as to the way their lunches etc go