Show UIPickerView text field is selected, then hide after selected

Swift 4 version

override func viewDidLoad() {
    super.viewDidLoad()

    pickerView.dataSource = self
    pickerView.delegate = self

    textField.delegate = self
    textField.inputView = pickerView
}

And the extensions

// MARK: - UIPickerViewDelegate

extension ViewController: UITextFieldDelegate {

    func textFieldShouldBeginEditing(_ textField: UITextField) -> Bool {
        pickerView.isHidden = false
        return false
    }
}

// MARK: - UIPickerViewDelegate

extension ViewController: UIPickerViewDelegate, UIPickerViewDataSource {

    func numberOfComponents(in pickerView: UIPickerView) -> Int {
        return 1
    }

    func pickerView(_ pickerView: UIPickerView, numberOfRowsInComponent component: Int) -> Int {
        return myItems.count
    }

    func pickerView( _ pickerView: UIPickerView, titleForRow row: Int, forComponent component: Int) -> String? {
        return myItems[row].name
    }

    func pickerView( _ pickerView: UIPickerView, didSelectRow row: Int, inComponent component: Int) {
        textField.text = myItems[row].name
        pickerView.isHidden = true
    }
}

If I understood well your question, you want:

1. Have an UITextField which display a text selected
2. Opening a picker when the user click on the UITextField
3. Close the picker when an item (in the picker) is selected, and set it in the UITextField

This is the complete code to manage it, you just have to link the delegate of your UITextField:

@IBOutlet var textfieldBizCat: UITextField!
@IBOutlet var pickerBizCat: UIPickerView! = UIPickerView()

var bizCat = ["Cat One", "Cat Two", "Cat Three"]


override func viewDidLoad() {
    super.viewDidLoad()
    pickerBizCat.hidden = true;
    textfieldBizCat.text = bizCat[0]
}

// returns the number of 'columns' to display.
func numberOfComponentsInPickerView(pickerView: UIPickerView!) -> Int{
    return 1
}

// returns the # of rows in each component..
func pickerView(pickerView: UIPickerView!, numberOfRowsInComponent component: Int) -> Int{
    return bizCat.count
}

func pickerView(pickerView: UIPickerView!, titleForRow row: Int, forComponent component: Int) -> String! {
    return bizCat[row]
}

func pickerView(pickerView: UIPickerView!, didSelectRow row: Int, inComponent component: Int)
{
    textfieldBizCat.text = bizCat[row]
    pickerBizCat.hidden = true;
}

func textFieldShouldBeginEditing(textField: UITextField) -> Bool {
    pickerBizCat.hidden = false
    return false
}

What I changed from your code:

• Used UITextFieldDelegate to display the picker when the UITextField is selected
• Hide the picker once an item is selected, and setup the UITextField
• Set the first row of your picker in the UITextField when any item is selected

How about in your didSelectRow method you resignFirstResponder?

func pickerView(pickerView: UIPickerView!, didSelectRow row: Int, inComponent component: Int)
{
textfieldBizCat.text = bizCat[row]
pickerBizCat.resignFirstResponder()
}