Millions of seniors rely on Medicare for health coverage during retirement. But one major myth surrounding the program is that it's free, or at least inexpensive.

Not so. Between premiums, deductibles, and copays, coverage under Medicare can constitute a major strain on seniors' budgets. And when we throw in the fact that original Medicare doesn't cover a number of key healthcare services like dental care, eye exams, and hearing aids, it's easy to see why so many seniors buckle under the weight of healthcare bills -- especially those who get the bulk of their income from Social Security.

It's not surprising, then, to learn that many seniors have been forced back to work for the express reason of needing money to cover medical bills. In fact, one in seven has taken either a part-time or full-time job to scrounge up the money to pay for healthcare, according to a recent survey by MedicarePlans.com. And for many -- especially those who were forced to return to full-time work -- that's far from ideal.

Masked man in front of shelves stocked with food.

Image source: Getty Images.

If you'd rather not land in a similar boat once you're retired and on Medicare, it pays to set aside money in advance to cover your future healthcare costs. Here's how.

Take advantage of the right savings accounts

There are different savings tools that let you set aside funds for healthcare in retirement while also enjoying tax benefits. First, you could put more money into an IRA or 401(k) plan. Though these plans aren't specific to healthcare expenses, once you turn 59 1/2, that money is yours to use for any purpose. With a traditional IRA or 401(k), you get tax-free contributions. With a Roth IRA, withdrawals are tax-free.

You can also fund a health savings account (HSA) during your working years and carry that money with you into retirement. HSA funds never expire and contributions go in tax-free. And the money in an HSA can grow in a tax-free manner, the same way Roth IRA and Roth 401(k) portfolios grow.

HSA withdrawals are also tax-free provided they're used to cover qualified healthcare expenses. And so if you do a good job of contributing to an HSA, by the time you're on Medicare, you may have plenty of money on hand to cover your various out-of-pocket costs.

Be sure to budget for healthcare

A big reason so many Medicare enrollees struggle with their bills is that they're simply not prepared for the costs that lie ahead. A better bet? Read up on healthcare expenses in retirement and do your best to save for them well in advance.

Fidelity recently estimated that the average 65-year-old opposite-gendered couple retiring this year will spend a whopping $300,000 on healthcare during retirement. And that sum accounts for the various costs seniors commonly incur under Medicare. The more savings you take with you into retirement, the easier it'll be to manage those costs -- and avoid a scenario where you're forced back into the labor market when you really don't want to be a part of it.