Movement after Haste is cast on you

I've been playing D&D for a few years and am very new to the 5.5e rules, as well as having a character that can be hasted. I have ran into a question I can't figure out.

How much movement would you have if you have Haste cast on you after you have moved all you could in a turn?

For example, your party member is holding their action to cast Haste on you when you get in range. Your speed is 30ft and to get in range you need to move 60ft. So you move 30ft and dash 30ft to get into range, then your party member casts Haste on you. How much movement do you have left, not counting the Hasted action? Zero? 30ft? 60ft?

I think it is 60ft because your speed is doubled to 60ft, but you used half of it already, so you have 30ft left. The Dash action gives you a movement bonus equal to your speed for the current turn. Since your speed has increased, that bonus should also increase as it is for the rest of the turn. So you should have an additional 30ft from the dash action as well.

The reason why I feel the dash action should also get the bonus is because abilities that reduce your speed, also affect the movement bonus from dash. Like if I take the dash action to move 60ft in a turn, but an enemy has Sentinel and hits me as an Opportunity Attack, my speed drops to 0, and so the bonus I get from dash also drops to zero.