If your business is open, tell people
Post your plans and hours on your website prominently (include on your contact page, your home page, etc.) and post to social media.
Share your efforts to keep people safe
I
n addition to taking all prudent precautions like washing your hands, identify your protocol to keep your business clean and sanitary then communicate what you're doing. Again, post it prominently on your website, share it to social media, hang a flyer on your door or windows. This is also a chance to share the processes you've had in place all along.
Many people aren't significantly changing spending habits, focus on them.
This situation has revealed that many people are completely freaked out while others are somewhat less concerned and accept that things must go on. Might I suggest that you don't worry about convincing those who are on the fearful side that they're mistaken, rather work to get the attention of those will are still planning to shop, go out to eat, etc.
Focus on those who are receptive to your message and create an oasis for them to experience some.
Up the personal attention
Most local businesses can't become ecommerce businesses but are there opportunities for you to provide personal shopper services? This may mean adding the option to do a video call with clients and a virtual store walkthrough.
Perhaps this is a chance for your business to create a subscription service like the many monthly 'boxes' that are now available.
In closing, this is a great opportunity to reevaluate your processes, your marketing, and your goals going forward. Make it easy for your community to participate and feel good about supporting your business.