Whites are the number one most violent users of guns in the US. In 2013 there were 11,208 homicides, 21,175 suicides by firearm. Suicide rates vary by race and ethnicity. In 2016, the rate of suicide among whites it was 18.15%. In contrast, the suicide rate among Asian/Pacific Islanders was 7.00; the rate for blacks was 6.35; and the rate among Hispanics was 6.38.
OK so you didn't actually cite a source. But I will:
Guns and Suicide: Racial Disparities in Gun Homicides and Gun Suicides
Let's look at some numbers here.
"For all 50 states plus Washington DC, the average rate of homicides using a gun of any type for whites was 15.88 homicides per 1,000,000 population, while the average rate of homicides using a gun of any type for blacks was 155.51 homicides per 1,000,000 population."
So blacks are 9.8X more likely than whites to kill someone else with a gun.
"For all 50 states plus Washington DC, the average rate of suicide using a gun of any type for whites was 83.68 suicides per 1,000,000 population; the average rate of suicide using a gun of any type for blacks was 31.0 suicides per 1,000,000 population."
Whites are 2.70X as likely to kill themselves compared to blacks.
In 2010 there were a total of around 11,100 homicides and 19,400 suicides.
Converting the above averages to percentages, that means white people killed themselves 14,000 times and other people 1,000 times for a total of 15,000 people killed (roughly).
Doing the same for black people, we get 9,900 other people killed and 5,200 times they killed themselves for a grand total of 15,100 people killed. So roughly the same.
Now let's look at that in terms of population percentages. In 2010 white people made up 72% of the US population while black people made up 13% of the population. So the group that is 5.5X more common caused about the same amount of total firearm deaths.
But yeah, white people are totally more violent gun users.