Readied actions use your reaction, which is available from the start of your turn.
A character taking the Ready action may, when the triggering condition occurs later in the round, use their reaction to take the readied action. Note that this is a reaction, not a bonus action, and there's nothing that restricts this to happening only after the character's turn ends.
But this usually isn't necessary, since players don't need to declare actions before they take any movement. A player can declare their character is moving a short distance to where they can see an area that wasn't visible, and then declare their action (or move some more).
Here are examples of both options in play, first using Ready:
Player: "Okay, I'm going to Ready an action to run back to safety if I see anything nasty, then I'm going to move around the corner. What do I see?"
DM: "You see a wererat, poised to throw a dagger at you..."
Player: "So that triggers my readied action, and I run back around the corner!"
DM: "Not before1 the wererat takes their own readied action and attacks ... the dagger misses you, and now you can move for your reaction."
Or their turn could go like this:
Player: "I'll move around the corner. What do I see?"
DM: "You see a wererat, poised to throw a dagger at you..."
Player: "Crap! Okay, I'll Dash and move back around the corner!"
DM: "The wererat takes their own readied action first and attacks ... it's a miss. You can continue with your turn."
While both of them achieve the same immediate result, the first option also (assuming the player has their character flee) consumes the character's reaction for the turn, meaning they can't (for example) make opportunity attacks later in the round. Also note:
- In both cases the player could still use a bonus action (casting healing word, for example) before ending their turn.
- In neither case does the player prevent the wererat from using their readied action.
So, while a player can Ready an action that is likely to be triggered on their turn, generally they are better off not doing that and just waiting to use their regular action.
1 The timing of simultaneously triggered reactions isn't strictly governed by the rules, so while the DM might rule that the wererat can attack before the PC moves away, they don't have to. They may choose to let whichever of the two had the higher initiative roll act first, or require a contested Dexterity check. Or they could rule that even if the PC has the higher initiative, they can't move out of range of the wererat's knife before it can attack.