[3][4] She set an 800 m junior record of 2:04.09 minutes in the heats at the 2010 Asian Games, but was again slower in the final, taking eighth place.

Moving into the senior ranks at the age of twenty, she placed 30th at the 2011 IAAF World Cross Country Championships.

[6] She won that event at the 2011 Asian Athletics Championships the following month (her first regional title) and also placed fifth in the 800 m.[7] In Rio de Janeiro's 2011 Military World Games, she was the 1500 m bronze medalist.

[8] Genzeb was one of three Ethiopian-born Bahrainis to be entered into the women's 1500 m at the 2011 World Championships in Athletics alongside Mimi Belete and defending champion Maryam Yusuf Jamal.

[10] She collected further medals at the 2012 Asian Indoor Athletics Championships, taking the 1500 m title and finishing second to Zhao Jing in the 800 m.[11][12] Following this she won her first cross country medal at the Asian Championship meet, taking third place in a Bahraini podium sweep with Shitaye Eshete and Tejitu Daba.