Originally Published: 26 MAY 21 05:19 ET

By Madeline Holcombe, CNN

(CNN) -- The story of George Floyd has ignited a movement. But to his girlfriend, "Big Floyd" was the man she loved.

While the US marked the one-year anniversary Tuesday of the police killing of a man whose death sparked months of reckoning over policing and racial bias, Courtney Ross remembered who Floyd was before the world knew his name.

He was a person who believed in inclusiveness, she told CNN's Anderson Cooper on Tuesday. He cared about standing up for people who needed help and for bringing people together, she said. And she hoped that is the part of his legacy that people will carry forward.

"He hated to see people struggle. He would help anybody he passed on the street," Ross said. "That's what I think this society needs right now. We need a lot of love, we need a lot of hope, we need a lot of what Floyd stood for."

The movement that arose after a former Minneapolis police officer kneeled on Floyd's neck for more than 9 minutes was celebrated Tuesday, as marches were held in his honor and the Floyd family met with lawmakers in Washington to discuss the George Floyd Justice in Policing Act, which is stalled in the Senate.

President Joe Biden had hoped it would be passed by the anniversary of his death, but his loved ones are hopeful in the progress that has been made and the steps they think will come.

"I think things have changed. I think it's moving slowly but it's making progress," his brother Philonise Floyd told CNN's Brianna Keilar. "I just want everything to be better in life because I don't want to see people dying the same way my brother has passed."

Floyd would not want his loved ones to be anything but optimistic, Ross said. So she remains hopeful, she said, though she feels like she has waited long enough for change.

"Listen to the woman that loved him and the person that knew him in Minneapolis and knew how much he loved this city and do something for him," Ross said.

The act in his name stalled

Shareeduh Tate, Floyd's cousin and president of the George Floyd Memorial Foundation, told CNN on Tuesday that the family feels uplifted by the racial reckoning, the conviction of former police officer Derek Chauvin, and the federal indictment of Chauvin and the other three officers involved in Floyd's death.

"From my perspective, when we lost him, it was a very personal thing for us initially and we had no idea the kind of impact it would have," Tate told CNN's Poppy Harlow and Jim Sciutto.

But, she said, "It was almost immediately seeing the fact that people were able to have conversations across diverse lines, people were able to talk about things that we never had a conversation about before."

Tate said that while she had wanted to see the George Floyd Justice in Policing Act passed by Tuesday, the family would rather wait until Congress can pass a substantive bill.

The bill includes provisions to set up a national registry of police misconduct, a ban on racial and religious profiling by law enforcement and an overhaul of qualified immunity for police officers.

L. Chris Stewart, co-lead counsel for the Floyd family, told CNN's Wolf Blitzer on Tuesday that he believes the bill will be passed.

"I know everyone is fighting about qualified immunity, but we also have to make sure we care about the provisions that stop Black people from being killed in this bill before fighting over how to sue a cop," Stewart said, adding that both Democrats and Republicans know the bill has to become law.

"Not only are you protecting African Americans who are being brutalized out there, but you are protecting good officers that are out there doing their job," he said. "The bill protects everybody."

And White House domestic policy adviser Susan Rice became the latest administration official to express optimism over its progress Tuesday.

"There is a very serious and constructive negotiation ongoing between Democrats and Republicans in the Senate," Rice said on CNN's "Don Lemon Tonight." Rice said as long as the negotiations between lawmakers in the House and Senate continue to make progress, she remains hopeful legislation can get passed.

Memorials and events honor Floyd across US

The NAACP kicked off Tuesday by holding a moment of silence for Floyd at 9:29 a.m. on its Facebook page to mark the 9 minutes and 29 seconds Chauvin knelt on Floyd's neck.

Members of Floyd's family were expected to attend memorial events in Minneapolis on Tuesday, according to a family spokesman. One of those events was a "Celebration of Life" which includes a day of games, food, inflatable attractions for youth and special performances by Grammy Award-winning artists and local talent.

Minneapolis was also responding to violence on Tuesday with reports of gunfire near the place where Floyd died, now known as George Floyd Square. One person has been hospitalized with a gunshot wound. The shooting happened about 3.5 miles away from the park where the "Celebration of Life" was being held.

Elsewhere, activists in Dallas organized a solidarity march and rally on Tuesday and the California-based Pacific Symphony is streaming a free concert in honor of Floyd.