Nobody (well, few of us) love self-promoting. It can sometimes feel narcissistic or self-indulgent. But people visiting your website need and want to learn about you, so it is your job to communicate that with them as genuinely as possible. The trend over the last decade has been for professional websites to often just read like a resume. But the point of having a personal website is to add more depth to your profile and help outsiders understand the person behind the long list of awards and accomplishments.
Tip #1: A personal bio should read more like a story and less like a resume.
People are more likely to remember stories you tell than a list of awards your received. Notice if your bio includes a lot of lists in paragraph format (they're still lists!). Avoid the pseudo-resume. Your website can include a separate page for just your resume or list of accomplishments if that is important to you, but it's not the place for your bio.
Tip #2: Think about "why" questions as much (maybe more than) "what" questions.
It's easy to list of things you do, things you're "interested" in, or things you have accomplished in your career. But often people are more interested in why you do the things you do. How was it that you wound up in the profession that your in? What motivated you to pursue that path? There might even be an interesting story there that you could weave in!
Tip #3: Avoid generic phrases.
Saying that you "are deeply passionate about your clients/patients" is not unique or memorable. So even though it may be true, it doesn't sound particularly authentic or compelling. This is why Tip #1 (telling stories) is so important. Rather than saying something generic like you care about your clients, or that you "work tirelessly for others," give a story or example that demonstrates how those generic statements are true.
Tip #4: Ignore format rules.
There are no rules that say your bio has to read in chronological order. There is no checklist of things you must include in your bio. There isn't any unwritten code that says it must be authored in a single, neat, 2-3 paragraph format. Some people do better with writing out bios in a Q&A format. Others may want to just focus on one to two things about them that are important and ignore the rest. Whatever format you choose, make sure it feels right to you and communicates the top 2-3 important things you want your viewers to know about you.
Tip #5: Find a bio you like.
If you come across a bio that resonates with you, break down what about it was interesting or compelling. If it was the structure, try gutting the bio (keep the structure) and insert your own narrative. Drawing inspiration from other websites is a great way to help you get started in writing that first daunting sentence.