Does it mean voltage across diode is zero?If yes, then is zero voltage across diode condition for forward bias?
There's not just one "ideal" diode. 

The simplest type (what I think you are talking about) has 0V across it if the polarity is such that current would flow in the direction of the arrow, and doesn't conduct at all if the polarity is reversed. 

A slightly more complex model has a fixed voltage drop (usually taken to be 0.6V or 0.7V) if it is conducting current, and does not conduct current if the voltage is less than the fixed drop. If you consider the voltage drop to have a temperature coefficient (around -2mV/°C) then you can roughly incorporate temperature effects. 

In either of the above two cases, to find out what the diode is doing, remove the diode as a thought experiment and see (it may be obvious or you may need to resort to math) whether the bias would be positive or negative. 

An even more complex type of ideal diode obeys the nonlinear and temperature-sensitive Shockley diode equation, with ideality factor 1. Most diodes are not that ideal, and the ideality factor is more like 2. You can also have different Is for positive and negative bias.

Finally, you can include ohmic resistance in the equation (which has a positive temperature coefficient), and you'll be fairly close to modelling diode behavior in most real situations.