Unless an item specifically allows it, you would not be able to use a bonus action to get advantage in this way.
While T.J.L.'s answer is excellent for showing what balance implications there are for a DM allowing 'Use an Object' to be used in that way, and Peter Chaplin gives excellent alternatives, I believe it's useful to walk through why these actions would not be covered by 'Use an Object'. I hope it can give you inspiration on what a Thief Rogue can do, and hopefully temper any feeling that you personally might be limited by the capabilities of other classes/archetypes.
'Use an Object' has multiple jobs. I'll let the PHB take it from here and then break it down (numbering is mine):
(1) You normally interact with an object while doing something else, such as when you draw a sword as part of an attack. (2) When an object requires your action for its use, you take the Use an Object action. (3) This action is also useful when you want to interact with more than one object on your turn.
So in summary, the 'Use an Object' action is:
- Barring #2, Not needed to interact with an Object when it's used as part of another action.
- The Action requirement of using Objects that explicitly need an Action to use
- The Action taken for interacting with an Object
The key takeaway is that unless an object explicitly has wording saying you can use it "as an action" (2) 'Use an Object' is for doing something to the object (3), not use the object to do something (1).
Looking at the suggestions
Throwing dust into the eyes of an enemy
Picking up the dust could be 'Use an Action'. Dust is not a defined object with an "as an action" clause, and you're trying to use the dust to do something (blind), not do something to the dust, so 'Use an Action' would not be applicable when throwing it.
Using tinderbox to light their clothing, hair, or fur on fire
The rules for Tinderboxes say lighting something "with abundant, exposed fuel--takes an action", with anything else taking a minute. Whether clothing, hair, or fur can be considered abundant and exposed fuel, is up to your GM. If it is, then you could light it with 'Use an Object'.
Using ten foot pole or quarter staff to poke and harass them
Neither item has an "as an action" clause, and it is trying to use the pole to do something rather than do something to the pole. Depending on intent, this would be a Help, Attack, or Improvised Action.
Using ropes and whips to attempt to trip them up or lasso them
As above, Ropes don't have an 'As an Action' clause and you are using the rope to do something, not do something to the rope. This would be either Help or Improvised Action depending on intent.
Throwing caltrops, ball bearings, or oil, under their feet
All three of these items have an 'As an Action' clause, so this would be fine.
Pantsing them or messing with their clothing in a similar way
This one is debatable and up to the GM.
'Use an Action' is for explicitly mentioned item usage, or doing things to objects. Of the strategies you mentioned, only the Ball Bearings and maybe the Oil could be used as a bonus action by a lvl 3 Thief Rogue in order to potentially get advantage. You could still do all of these things as other actions, though. You could do it to help your team, or maybe they'll be disadvantaged long enough to last into your next turn and you'll have advantage at that point. It's not that they can't be done, only that it can't be done as a Bonus Action using Fast Hands.