In an AC coupled Op-Amp circuit where do input bias currents flow from?
Indeed Ib+ in the 2nd drawing is indeed flowing out of the ground.

There is nothing strange about that but you need to realize that in order to draw a current "out of the ground" and through a resistor (or an opamp input), you would need a negative voltage.

So the opamps used in the circuits you show need a negative supply rail assuming that the opamps have a biasing current which flows into the opamp.

There are also opamps which have a biasing current flowing out
 of the inputs (yep, sounds weird!) for example the LM324. This opamp is designed so that it can work without the negative supply voltage but still work with its input voltages close to the ground voltage.