Just curious I like to know if one fine day our Sun turns into a white dwarf at the later stage of its life, would the magnetic bubble, heliosphere gets thinner and eventually disappear? also at this moment is it changing in size?
Yes the heliosphere will disappear. As you know, the heliosphere exists due to the solar wind, which consists of charged particles that follow the magnetic field lines starting from the Sun and extending far into the universe (of course at some point they return to the Sun, as the loops need to be closed, but it's so far away that we usually assume it to be at infinity). Now when the Sun goes Red Giant and then loses its outer shells (planetary nebula), it will become a white dwarf. Then there won't be any wind originating from its surface and therefore there won't be any "magnetic bubble" left. The heliosphere stays roughly the same in size as long as the Sun remains in its Main Sequence stage, as a star remains relatively stable during this time of its life.