It's not necessarily a difference in personality. Don't forget that Kasumi's bike was STOLEN while FISHING. You save someone by fishing him out of the river and then he steals your bike. When you see your bike again, it's destroyed. Haruka's case was that she saw the bike accidentally destroyed, but she left it where it was. Both bikes were stolen but Kasumi's was STOLEN.
If anyone rode their bike to get to a water site to fish and gets his/her bike stolen, you wouldn't be happy regardless. The destruction also wasn't known to Kasumi. She didn't know Pikachu had a near-death situation and used a Thunderstorm to clear a horde of Onisuzume. Haruka witnessed Pikachu directly in trouble, and saw how the whole thing went.
Again, Haruka's case was "oh no my bike got destroyed, oh well." Kasumi's was "Darn it Satoshi, I fish you out of the water and you steal my bike and after I found it somewhere in the field it was fried." Kasumi didn't know where her bike was initially! She had to find it (oh and the fact that Satoshi disappeared from her sights until she found him again at the Tokiwa City Pokemon Centre).
Difference in personality, yes but conditions were also different. Anyone who had their bike stolen, then finding it destroyed in the middle of a field where nothing really is, would be rather frustrated (not to mention ending up carrying the bike all the way over to the city). Haruka knew Satoshi's conditions (professor explained it in a nutshell, sort of), but Kasumi didn't. So yeah, indifference to caring? Hm. I think being angry over your bike getting stolen and then found destroyed to be quite reasonable.
Oh and even if Haruka's bike being destroyed seemed unoriginal, if it weren't destroyed she would have her bike to ride back home (or anywhere else for that matter), and wouldn't have extensive walking problems. There wouldn't be a normal situation to join Satoshi. Leave a destroyed bike, sure. Leave a perfectly good conditioned bike that you enjoyed riding all the way over, no.
Of course the writers could have just had Haruka walk to Mishiro Town, but then it's far more practical to ride there (and Haruka riding the bike and then going WHOO! while jumping over a small ramp has a much better entrance appeal. And of course you can crash into a tree after seeing a Ghost by losing control of your bike, whereas walking you can't crash like that at all.)
Having Haruka run would also make little sense, even though it would match the R/S game running ability rather well.
So you sort of have to have the bike there and have it destroyed.
Oh, and Haruka's bike being destroyed seemed like an "opportunity to travel with an 'experienced trainer'". Whereas Kasumi wanted repayment of her bike from an "inexperienced trainer" who didn't even take care of Pikachu well (first impression-wise). Again, there's a large conditional difference, despite them both being Pikachu-emergencies (Kasumi's case was "alone". Haruka's case was "full assistance".)