My local newspaper has a policy to only include the race of crime victims or suspects if it is clearly relevant, such as when police suspect the crime to be a racially motivated hate crime. So in your example, a black man running over BLM protesters is not a racially motivated hate crime, so the suspect's race is not relevant. A white man commiting the same crime might be, or might be suspected to be, depending on the other facts of the case.
This is how it should be - and I suspect, as it usually is.
The most common type of crime when it comes to race is white-on-white (Source: publicly available FBI murder statistics), but you never hear about that because... well, it's normal, so no one bats an eye when a poor white person kills another poor white person(unless there's another aspect of the crime that makes it rarer/more newsworthy). Ditto Black-on-Black crime, except when it comes from someone trying to defend corrupt police departments. We life in a society that still has a high degree of de facto segregation, so this shouldn't be entirely surprising.
Race really shouldn't come into play unless A) the suspect is still at large, and race is relevant to identifying the perpetrator, or B) there's reason to believe it's related to the incident in question. Bonus points for C) It's captured on camera so it's obvious. Somehow there just aren't that many videos circulating of police using extreme, unnecessary force against white victims, despite the fact that 1) there are more white than black citizens in this country, and 2) More total crimes are committed by white citizens than black citizens in this country. It's extremely unlikely that cops have been caught on video abusing white victims nearly as often as they've abused black victims - because that shit would be all over the internet.
I think media companies are becoming increasingly incentivized to put out stories that will be shared throughout social media.
I think the bias is incidentally racially biased, but more to the point, it is biased toward the most profitable emotion for them - outrage.
I do think there's a a degree of truth in this - media companies will put out whatever sells. However, "Whatever sells" looks quite a bit different depending on whether your're CNN, MSNBC, Fox, or OAN.