Of course they prefer Seattle, unless they are hanging out in Magnolia, they aren't going to be arrested with the explicit purpose of getting dumped somewhere else. It pulls double-duty, through shelters and services because NIMBY's in the suburbs are happy to export all their problems to it.
And most homeless don't regularly get arrested for violent crimes, but it's incredibly telling that you immediately turn the conversation to the most problematic minority, and ignore how your suburb shits on the other 90% of them. Just because you're homeless doesn't make you a violent criminal. (Just like how if you're from the Eastside doesn't immediately make you a lot of other unsavory things.)
There are ~11,000 homeless people in King County. Most of them aren't violent criminals. How many does Bellevue house? Your fair share is ~700, are you meeting it? Seattle's fair share is ~3,400 - or it would be, if you weren't shirking yours.