Workplace issue

i have recently resign from the job as i had an issue with department boss.was feeling there demotivated...now i am unemployed...when called hr for clearance..he said if the reason behind ur resigning is the issue with dept boss,sort it out and if u could consider for rejoining,we can go further. Now the thing is for this i need to talk with my dept boss and apologize him.i could be back on job..but its really embarrassing to work there after happening such things,what about reputation...i am confused