Does inertia increase with speed?

I have heard that when the speed of the object increase, the mass of the object also increase. (Why does an object with higher speed gain more (relativistic) mass?)

So inertia which is related to mass, increase with speed?

So, if I accelerate on a bus, my mass will increase and my inertia will increase for a while on the bus, until the bus stops?

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@nonagon How negligible is it? If it travels at 100km/h? –  owlp May 15 '13 at 9:10
"The Inertia of Energy": mathpages.com/rr/s2-03/2-03.htm. The exact proportionality between the extra inertia and the extra energy of a moving particle naturally suggests that the energy itself has contributed the inertia, –  Alfred Centauri May 15 '13 at 12:45
Please read en.wikipedia.org/wiki/… to the end of the section. –  firtree May 15 '13 at 12:46

If we interpret the inertia as $F=ma$, then 'yes' again: it increases with a factor of $\gamma$ in the transversal direction, and with a factor of $\gamma^3$ in the longitudinal direction. But if we interpret inertia as $F^\mu=ma^\mu$, then it does not change. –  firtree May 15 '13 at 12:40