How much money are we talking about? Not knowing to within 10 million dollars is Not Plausible unless the net worth is on the order of 100 million or more. I can't speak to how to present such a character, but I don't think you _can_ present such a character without addressing the implications of being that wealthy in some detail.
What is the form of the money? Is it shares in a private concern that can't be sold on the open market? Cash under the mattress? Gold coins in a safe? Portfolio in one or more brokerage accounts? Are there financial service professionals involved (tax preparer, accountant, broker, financial planner, etc.)? If stock, what is the investment strategy of the character: buy-and-hold, day-trader, whimsical? Have they authorized their broker (or someone else) to make trading decisions on their behalf? If their money is in the form of a real estate empire, who collects the rent and calls people to make repairs/do buildout for new commercial clients, etc?
How did the character acquire the money? Did they inherit some or all of it? From who? Was it through a will or a trust? Are there trustees? Are there constraints on their access to the money and/or how it can be invested?
If the character has become wealthy or wealthier through their own activities, what were they? Retired courtesan? Lottery winner? Successful inventor? Embezzler? Cheating at faro? Betting on the horses? If they made the money by investing or by some business of their own, how did they get their seed money? Who did they work for/who worked for them along the way? What kind of relationship do they have with the people before/during and after getting wealthy or wealthier?
What is their run rate? How much do they spend monthly on rent/car/food/entertainment/hookers/coca
How do they access their money? Debit card on a brokerage account? Automatic transfers to an ordinary checking account? Credit cards paid by checks on the brokerage account? Clandestine deliveries of gold bullion? A magic wallet full of unlimited $50 and $100 bills (gold sovereigns, guineas). Possibly the most annoying problem with rich people in novels is that they don't seem to have to deal with ordinary financial instruments. Which may be plausible for the spectacularly wealthy, but isn't plausible with a garden variety multi-millionaire.
I have no idea if Heyer is historically accurate. What I do know is that Heyer manages to convey in some detail how the wealthy people in her novels get along. And when they do something weird like take a surprise trip to Paris without their luggage or bank drafts, they pawn their jewelry for something to pay the inn for bed and board. You don't get distracted for fifty pages in a Heyer novel trying to figure out how the hero is funding his activities. You _know_. Loretta Chase did a reasonable job of this in _Lord of Scoundrels_ and even did a nice job of depicting how the not-wealthy often have no idea about how things work amongst the wealthy, and how people can exploit that ignorance by revealing misleading information.
I should also note that this information doesn't have to all be presented in the course of the novel. But the author should know this stuff about all of the characters, rich or poor, and this backstory can inform the actions of the characters. So I don't have to wonder if that mail is still sitting in the snow, and where the car is, and why the heroine didn't have any credit cards, and whether she has a financial advisor, and why she didn't have a lawyer to call for advice about her divorce. After all, she's that wealthy, she ought to have a will or whatever. And if she's got one of those, she's got a lawyer she used for that. And that lawyer probably works at a big firm and if they don't, they're still a potential source of recommendations for divorce lawyers.
And damn, anyone worth 50-60 million dollars ought to be able to hire some fucking amazing security if she's worried about her soon-to-be-ex-husband coming after her. She should _not_ have to rely upon witness protection from the police.
There are a number of ways this information could be presented in the course of the ordinary business of a romance novel. Usually, there are secondary characters in whom the romantic leads confide along the way about their budding relationship. A character with a real estate empire who is involved in management of the properties (let's say she's got several small apartment buildings) might strike up a conversation with the genial older person who answers the phone and opens the mail and deposits the rent checks. Sometimes, something unrelated to the developing relationship crops up unexpectedly and causes a character to behave differently or be unavailable to Their New Other Half, resulting in suspicion and and argument. An urgent call regarding impending financial doom -- say, an IRS audit -- requiring the character's immediate and ongoing attention, particularly if it threw that character into close partnership with someone attractive of the appropriate gender. OTOH, this could also be the rationale for getting Our Couple together in the first place.
Yeah, like we're ever going to see a romance novel in which one of the characters is the sole proprietor of some business and the other character is an auditor for the IRS.
But it would be cool. Other possibilities: SEC investigator and an investor whose psychic abilities enable them to generate returns in the stock market otherwise only explainable by insider trading.