… you don’t have a letter of recommendation from your main supervisor?
I swear, she is hopeless when it comes to reference letters! She’s written a couple for me for grant applications etc and they were no longer than 2 lines… 2 lines!!! It basically said hi yeah please support her application but not why I deserved it.
Aren’t they supposed to like talk about your skills and personality etc and basically sell you in the letter? I am working on a really important application for which I need 3 academic referees to write me a letter and I just don’t want to ask my main supervisor to do it. Unless I actually tell her how to go about writing the letter which I’m not sure how to say to her.
Re: Does it look bad if…
I don’t know if it’ll look bad or not but I certainly do think that it’ll look great if you do have one from your supervisor.
My under grad supervisor was a busy busy guy and I needed one to apply for my MS program. I asked him twice to write one for me but he politely said that he hasn’t got much time to write it so why don’t I write a draft for him and then he’ll go through that and make sure I get my recommendation letter. 
And guess what, I got an awesome recommendation letter!!! 
Re: Does it look bad if...
It is a common misconception that letters from prominent/well-known personalities help alot when it is not the case. A good letter of recommendation should highlight in detail your strengths and weaknesses and preferably should highlight an instance where you displayed your positive qualities. A comprehensive LoR from a customer/client would be a better option than a 2 liner/generic LoR from your supervisor.
In your case, what you can do is that write the letter yourself and get it signed from your supervisor. May not be ethical but a lot of people do it and in Pakistan, professors/supervisors actually ask the applicant to write it themselves. If you are not okay with this option, find someone who knows you well and has available time to write a comprehensive LoR. Do keep in mind a timeline of 2-4 weeks for this whole process. I was in for a shock myself when I didn't receive a single LoR from my professors & supervisors for a month despite constant reminders
Re: Does it look bad if...
If I wer eyou , ask if you would like to draft a letter on her behalf, it seems like blowing your own trumpet but saves on time waiting for procrastinating supervisors