Don't start spending money on expensive saddles just yet.
That discomfort is normal for the first few weeks if you've not cycled for a while. Cycling aside, that short section of the body does not have to deal with any pressure in any other walk of life. When you sit on a chair, your sit bones take the pressure.
It really is a case of toughening it up. If you ride 2 or 3 times a week expect pain for about a month.
If you're still hurting after this time, then think about a new saddle.
By the way, you can ease saddle pains by using greasy creams - petroleum jelly or nappy creams. They help reduce the friction between you and the saddle.
Also, have a look at your saddle - is it too low, too high, too far forward, too far back.
There are three contacts points on a bike - hands, feet and arse. All three should take your weight equally. If one is carrying more, it'll hurt more.
Too low a saddle means you're sitting more, which means more pressure on the soft tissue mentioned. Too high saddle means you're being pushed forward more which increases pressure on palms and wrists.
Hope this helps.