then how about an bomber specific more powerful engine based on kaveri?
You can not simply develop anykind of engine out of Kaveri, it was developed for certain purposes and with certain specs in mind. For more powerful engines, that can be used on such aircrafts you have in mind, you need to make a complete new development. The whole point of a new engine based on Kaveri is mood anyway, since you normaly base new developments only on it, if the earlier was successful, but since it was a failure!
What they now have in mind is downgrading the current engine, to be used without AB and with less performance requirements in the AURA UCAV, but even that will be difficult enough, because of the size and weight restrictions.
If Kaveri would be useful as a base for another important development, the most logical choice would be to develop a higher thrust fighter engine for FGFA from it. But as we know, DRDO is not even able to further develop it to the 90 to 100kN (AB thrust), required for LCA and AMCA.
^^ i have already said that this bomber can be used as nirbhay ALCM launcher
with a range 0f 8,000 Km (non refueled) and 15,000 KG payload (both speculated by me) it can carry 10 to 12 Nirbhays
remember a MKI can carry just 3 nirbhays with 1,000 KM range
so this bomber can pack punch of 4 to 5 MKIs and with 100 to 120% greater range
or it can carry 6 to 8 Nirbhay 2 with 2000 KM range (note this is imaginary version by me)
You only count numbers here, without looking at the operational advantages and disadvantages of this scenario. A bomber is big, heavy and slow, especially when loaded with so many heavy missiles. It would be detected by Chinese radar or AWACS even before it enters their airspace and can be easily intercepted. That means it needs a lot of escort fighters to protect it, or as other members said, air superiority! In both cases, it would need to fly a long way till it gets in range to fire the missiles to any important targets, that again means a lot of time to be intercepted by air or ground targets.
All this explains why bombers have no importance for IAF from tactical reasons and why improve missiles and deep strike fighter capabilities for the mid ranges (Tibet area) are more important.
Even an MKI that in theory could carry 3 of such missiles, would practically carry only 1 or 2 at max, because you simply use more fighters, with lower numbers of weapons, to remain with better performance and spread the attack capability.