Tenuous wind bubbles , which are formed by the spin-down activity of central compact remnants , are relevant in some models of fast radio bursts ( FRBs ) and super-luminous supernovae . We study their high-energy signatures , focusing on the role of pair-enriched bubbles produced by young magnetars , rapidly-rotating neutron stars , and magnetized white dwarfs . ( i ) First , we study the nebular properties and the conditions allowing for escape of high-energy gamma-rays and radio waves , showing that their escape is possible for nebulae with ages of \gtrsim 10 - 100 yr . In the rapidly-rotating neutron star scenario , we find that radio emission from the quasi-steady nebula itself may be bright enough to be detected especially at sub-mm frequencies , which is relevant as a possible counterpart of pulsar-driven SNe and FRBs . ( ii ) Second , we consider the fate of bursting emission in the nebulae . We suggest that an impulsive burst may lead to a highly relativistic flow , which would interact with the nebula . If the shocked nebula is still relativistic , pre-existing non-thermal particles in the nebula can be significantly boosted by the forward shock , leading to short-duration ( maybe millisecond or longer ) high-energy gamma-ray flashes . Possible dissipation at the reverse shock may also lead to gamma-ray emission . ( iii ) After such flares , interactions with the baryonic ejecta may lead to afterglow emission with a duration of days to weeks . In the magnetar scenario , this burst-in-bubble model leads to the expectation that nearby ( \lesssim 10 - 100 Mpc ) high-energy gamma-ray flashes may be detected by the High-Altitude Water Cherenkov Observatory and the Cherenkov Telescope Array , and the subsequent afterglow emission may be seen by radio telescopes such as the Very Large Array . ( iv ) Finally , we discuss several implications specific to FRBs , including constraints on the emission regions and limits on soft gamma-ray counterparts .