In order to establish authority and trust on social media it's very important to write a professional sounding bio for your profiles. When someone finds your account and is deciding whether or not to start following you and whether or not to follow your suggestions to buy X product, one of the first things they will do is to check your profile and to see what you're all about. They will then make up their mind on this based almost entirely on your bio. So you better make sure it sounds professional and compelling.
Professional vs Personal
If this is a business account and you're trying to attract customers, network or otherwise build yourself a reputation then you should make sure to use a professional tone. That means avoiding flippant remarks, using professional terms and checking your spelling and grammar. Just a little personal tidbit thrown in for good measure won't hurt though. Remember that social media is personal in nature.
Make sure you avoid using lots of jargon and buzzwords. Your objective is not to sound clever here. You want to be clear and precise about what it is that you do.Less is more, so be frugal with your use of words and use short sentences. Especially if there's a word limit like there is on Instagram.
Think About Your Audience
If you're still having a hard time finding your 'tone' then imagine your target market/customer avatar that you are marketing to. Maybe you even know someone in real life who fits into the right demographic. Keep them in mind then imagine you're writing directly to them.
Don't Repeat Yourself
If this is LinkedIn, then you'll have a chance to show your accomplishments later on. If it's Facebook, you can include details about your business in other sections. This should be an overview that is efficient in telling people who you are, and that efficiency means avoiding covering ground that will be addressed later.
Leave a link to your social media in the comments below so I can see your bio!