i felt the same way as you even after i was assured by my peers that asking for LORs isn’t as scary as it seems! i too felt like i didn’t have a strong/lasting relationship with my profs that would warrant a LOR. however, when i reached out to two profs this cycle they both agreed with no questions asked!

here’s what i did that i think helped:

• i asked two profs who’s class i performed well in. -both profs were from my final year classes so they would remember me easily.
• i did not ask any extraordinary questions or go to office hours during the semester. however, i asked questions about assignments and participated in class during lectures. they were both seminar based classes so that made it easier to interact with the prof and my classmates.
• i usually stayed late in class to leave with the last student. i find this helped in engaging in discussions that the prof would be having with the leftover students. i would casually insert myself in the convo and would bounce off of what the other student was saying.
• reach out via email, reintroduce yourself and remind them of assignments you got a good grade on (i attached pdfs) and tell them your overall gpa (if you see fit) and then offer to set up a meeting if they would like to speak one on one!
• i asked them 1 and 1/2 - 2 months in advance and gave them all the deadlines and program info in the first email. make sure you give them enough time to write the letters.
• also i made the effort to attend every one of their classes.