So what makes a good blues musician?

Good question.  A wide range of skills, knowledge and experience, and professionalism.  

We can't all hope to have all of them.  We all have different strengths and weaknesses and different personalities.  But there are obviously some core skills that will make life easier as a blues musician if you have them.  

Technical ability on your instrument,  knowledge of the blues scales and modes to the point that those are internalised and you can play them at will.  Good listening skills - to identify the changes in chord progressions and - especially if you play a melody instrument - great improvisation skills.   I have been pracising this in class and at home.  You tube has great resources, including blues recordings from all the greats, blues backing tracks and improvisation lessons and tips.

This means not just having the technical ability and theory but being creative, flexible and relating well to other musicians.   This only comes with practice, practice and practice and needs discipline, organisation and commitment.  You need to build your blues repertoire and knowledge of the blues so if someone asks you what you think of a blues style you can hold your own.

If gigging you need performance skills, the ability overcome nerves and to focus and, of course, reliability.  Always be professional and on time,  dress appropriately for the venue/audience be polite and polish introductions etc.  
Do your research on styles, riffs, lyrics etc and be secure about what you intend to play - with some extras.  

Pay attention to the business side too with business cards and your contact details.  You never know who might be in the audience and want to employ you.  Network if possible to build your profile and increase your chances of follow up work. 

Have a good time - the blues is all about being steeped in the music.