Would it look bad to negotiate a job offer if they've topped a job offer I've declined from elsewhere?

Last week I got a job offer from company A but I was in final stages with another company and still waiting for their decision. So I emailed company B to let them know I've got an offer that I needed to respond to within 2 days, and was wondering if they'd be firming up their decision anytime soon.

Company B couldn't get back to me before company A's deadline, and for a few other reasons I didn't move forward with company A's offer.

The next day company B rang me and asked for A's offer details, so I told them the base salary & sign on bonus that A offered (which was pretty good to be honest).

After that company B came back and made me an offer with a higher salary & sign on bonus than offer A. It's really good money and I'd be silly not to take it.

However, company B is in a different industry than company A and is a much larger company. According to glassdoor their salary ranges are higher than company A's (though there aren't very many salaries posted so not sure how accurate/representative they are). And the salary they offered me is at the lower end of the range for this position.

The general advice in negotiations seems to be to never accept a company's initial offer as they'll always lowball you at first. But also don't keep increasing your demands or play games as it'll leave a sour taste in their mouth.

At this stage will I look greedy if I negotiate the base salary? I feel like if I never got offer A, company B might not have offered me this much money, so in a way I've kind of negotiated already?

But I don't want to negotiate just for the sake of it and risk coming across like I'm greedy or rude.

They know I've already declined offer A and don't have any other offers in hand (but in mid/early stages with a few other companies).

What should I do? Thanks for your advice.

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