As the question states, if a creature has blindsight, do they have disadvantage on a target that is within the range of their blindsight and not otherwise hidden/covered?

The wording of the invisible condition suggests that attacks against an invisible creature have disadvantage AND the creature can't be seen without magic/special sense not BECAUSE the creature can't be seen.

Invisible Condition

An invisible creature is impossible to see without the aid of magic or a special sense. For the purposes of hiding, the creature is heavily obscured. The creature's location can be detected by any noise it makes or any tracks it leaves.

Attack rolls against the creature have disadvantage, and the creature's attack rolls have advantage.

The Special Sense Blindsense bypasses the mechanics of being Invisible

The Invisible condition states (emphasis mine):

An invisible creature is impossible to see without the aid of magic or a special sense.

Blindsight is a special type of sense, along with senses like True Sight and Tremorsense.

The condition explicitly calls out that there are special senses that bypass the condition. As Blindsight allows a creature to see the unseen, being invisible is bypassed by that sense and thus the mechanics that the Invisible condition provides are not activated.

Jeremy Crawford also provides some support:

Blindsight lets you spot an invisible creature in range, but that creature can still try to hide behind something with Stealth.

Once you can see the creature the effects of being Invisible are no longer active.

No, it doesn't have disadvantage.

A creature with blindsight can perceive its environment without using sight. Therefore it can perceive invisible creatures.

"Invisible" means "unable to be seen". The Invisible condition is actually defined that way:

An invisible creature is impossible to see without the aid of magic or a special sense.

So if someone can effectively see you, then you aren't invisible to them and the adverse effects of the Invisible condition don't apply to them. Note that there is precedent for being subject to a condition with respect to only some creatures: you are considered blinded when trying to see things that are heavily obscured.

The rules handle attacks between unseen characters in a consistent way, whether they're invisible, blind (and thus unable to see anything), or heavily obscured.

An Invisible creature is still Invisible even if someone can see it

Invisibility is a condition that certain magical effects (e.g. Invisibility spell) gives you and the condition only ends in the way that the effect says - I don't know of any that end just because something can "see" you. While you have the condition it does what it says it does.

So, yes, an Invisible creature attacks with advantage and is attacked with disadvantage even if the target/attacker can "see" it through blindsight, tremorsense, truesight etc.

Why? Because the advantage/disadvantage comes from the Invisible condition (PHB p.291) and is distinct from the advantage/disadvantage that comes from being unseen (PHB p.195).

Does this make sense? I don't ask that question anymore.