If when we go to sleep and the bard wants to steal the item from me while I am clutching it in my sleep, holding it to myself, how easy would it be for them to steal it from, what kind of rolls would be needed here?
If the bard is trying to steal something from you in your sleep, generally the way I as a DM would run this is first they would have to make a stealth roll contested by your passive perception to see if they can get near your character without waking them. This would then be followed by a sleight of hand check for the actual theft. Sleight of Hand is listed on page 177 of the players handbook as a check used to
“lift a coin purse off another person or slip something out of their pocket”
making it the skill that best matches the situation you describe. The difficulty challenge is up to your DM but generally the thresholds set by the players handbook on page 174 is:
- Very easy - DC 5
- Easy - DC 10
- Medium - DC 15
- Hard - DC 20
- Very Hard - DC 25
- Nearly impossible - DC 30
Factors affecting your DM’s decisions should include size, weight and how noisy the object might be when moved.
However, I would ask how you as a player feels about having your possessions stolen by another player. It is general convention (at least at my table and a lot of the questions I see on this and other sites about my guy syndrome. For example, this rant is a little long but encapsulates some of the issues that parties screwing each other over can cause) that stealing from other players can lead to bad feeling among the party. It may be worth talking to the player or your DM about how this is going to affect the dynamic at the table before this goes ahead.
RAW, It depends how perceptive you are
To steal something from you, the bard would make a Dexterity (Sleight of Hand) check contested by your Passive Perception. Your Perception check would likely be made at disadvantage (-5 to a passive check) since you are asleep. Therefore, how difficult it is to steal something from you is (by RAW) entirely based on how perceptive your character is.
There are bigger issues
That said, stealing from another player is something that varies from table to table. It is something that should be discussed in session zero. It should also be discussed if and when if become an issue as the table. As V2Blast brilliantly puts it in the comments on your question:
While this is a valid question, if you're worried about party members stealing from you while you're sleeping, there are bigger problems in your group dynamic that are probably worth asking about directly.
If this is something that bothers you - in fact, even if it doesn't, but is happening at your table - I suggest you discuss it with the DM and other players to reach an agreement that everyone feels comfortable with.