Can a character sneak up on another character who has blindsight? Can I just make a stealth check to hide from blindsight?
Only if you have cover (or are out of combat)
Blindsight receives two definitions in the Rules Compendium, with slightly different wording.
Blindsight: A creature that has blindsight can see normally regardless of how obscured1 an area is and regardless of whether creatures or objects are invisible. Blindsight usually has a radius, beyond which the creature relies on its other senses.
Rules Compendium pg. 168, Chapter 5: Exploration and the Environment. Superscript added.
blindsight: A creature that has blindsight can clearly see creatures or objects within a specified radius and within line of effect, even if they are invisible or in obscured1 squares. The creature otherwise relies on its other senses.
Rules Compendium pg. 309, Glossary. Superscript added.
What can be taken from this is that Blindsight essentially allows the creature to ignore all forms of concealment, whether from darkness, obscured squares, or invisibility, and can perceive creatures as if those conditions didn't exist. Just as a person standing on open ground would be unable to use Stealth to become Hidden under normal circumstances, an invisible person on open ground would be unable to use Stealth to become Hidden from a creature with Blindsight.
However, unlike Tremorsense (which explicitly says otherwise), Blindsight requires line of effect and does not allow a creature to ignore various forms of cover. Thus, as it's possible to gain the Hidden state with superior cover and maintain it with partial cover, one could duck around a corner to hide and - terrain permitting - sneak up to the target using cover to maintain the Hidden state. The normal Stealth skill provisions for sneaking up on a distracted creature without cover or concealment outside of combat also still apply, offering another alternative.
Related information: What are the "normal requirements" to hiding?
1"Obscured" refers to the specific terms "lightly obscured," "heavily obscured," and "totally obscured," which are used to describe levels of concealment in forms other than darkness, and do not include cover.
According to the 4e definition of Blindsight:
Blindsight: A monster with blindsight can perceive creatures and objects within the stated number of squares, making Perception checks as normal. The creature automatically fails Perception checks to notice things outside of the range of its blindsight.
So according to raw, if you stealth into the range of it's blindsight, they can still make a Perception check to locate you. Note, it does not say they automatically perceive someone/thing within their sight range. So theoretically yes, you can sneak up on a creature with Blindsight, especially if you have a high enough sneak vs. the creatures perception.