House Elves are a Known Problem in HP fanfiction, as their demonstrated capabilities are
substantial and yet apparently literally no-one
ever uses them for anything other than basic housekeeping. This is because, much like Time Turners, House Elves are a result of Rowling adding an element into the story for purely narrative reasons and just not bothering to consider the wider consequences of that element in the setting as a whole. As such, even a quick thonk can easily come up with dozens of ways to use a House Elf or two to
easily solve pretty much the entire plot in about ten minutes flat.
The only real ways to get around this are to either ignore canon entirely regarding what House Elves can do, tie yourself into knots explaining why House Elves can't do things that they are outright shown to do in canon ('Dobby is insane by House Elf standards, normal Elves would never attack a Wizard even though they theoreticcally
could' is the most common way of doing this that I've seen), or just declare that wizards are fucking stupid and ignore House Elves out of prejudice.
e:
Why would she even need to send bombs via elves anyway? Every single one of her targets is muggle-hating and don't consider them a serious threat, so she could just send them bog standard nonmagical mail bombs via owl mail and take out basically everyone she can send a letter to who opens it... which is everyone in the wizarding world since there's no way canonically to block owl mail IIRC and there's no way to detect nonmagical explosives via magic. The only person I can think of who wouldn't die from this would be Moody, and that's because he's paranoid and wouldn't open it himself and because he has a magic eye that can literally see through the package coupled with what seems to be a pretty decent understanding of the muggle world.
Owls can be intercepted through the basic method of 'see owl, intercept owl', and in 5th year Hogwarts instituted a policy of inspecting all Owl Mail instead of letting students just receive it in the Great Hall etc, which implies that it
is possible to block or redirect Postbirds, as otherwise they should have just kept delivering things straight to people as they are shown to do throughout the books.
The fact that Hedwig was easily able to locate Sirius while he was on the run while Aurors could not, and that apparently no-one ever thought to send Sirius Black a letter and just
follow the Owl, suggests that this is yet another of Rowling's
many 'I didn't think the consequences of this existing through' moments.
Rowling
did 'answer' this in an FAQ, but, well:
J.K. Rowling Official Site FAQ said:
Q: In 'Prisoner of Azkaban', why couldn't the Ministry of Magic have sent Sirius an owl, and then followed it, to find him?
A: Just as wizards can make buildings unplottable, they can also make themselves untraceable. Voldemort would have been found long ago if it had been as simple as sending him an owl!
Which does not actually answer
anything, nor does it explain how Hedwig could find Sirius when everyone else could not.