How much, and what, you need to know will depend on the job you are applying for.
If you aren't going to leverage your additional knowledge from the bio side of your degree, you are likely to be at a disadvantage compared to the pure-computing-degree folks, so I think you really do want to look for positions where that combination of skills is needed.
I'm a bioinformatics researcher, it's a very diverse field and I didn't come at it with a Biology background at all. I can't really comment about graduate recruitment in bioinformatics as most come into research with a masters or PhD. However you could try approaching research groups at your current University looking for short term projects/internships (probably unpaid). I've known several people get jobs from that.
With regard to bioinformatics programming skills, from my experience Python, Perl and R are very highly used.
If you're not interested in bioinformatics at all and are looking for programming jobs I agree with keshlam, you are likely to be at a bit of a disadvantage.
I know little to nothing about bioinformatics, but I believe it is not very relevant in this case.
You mentioned several programming languages that you have learned in college, and several that you're still learning. That's good, but I learned French at school and I can't have a conversation in French.
I believe the core of your question is your insecurity; you are in doubt of your skills. This is a valid concern, but one that will not help you find a job. The fact that you asked this question on a forum like SE, does however help as it shows you are aware you may need help and you ask for help. Asking is always appreciated.
I can only speak for the Netherlands here, but I'm sure this case would be similar in many other western countries. So, here we go:
The fact that you're getting a bachelor's degree proves that you can learn at at least the given tempo, but it does not prove much more than that.
For someone looking for a first job as programmer, most companies I know care much more about what you do with your spare time. If you don't know something, that's not bad, as you can still learn on the job, as you have already proven with your degree. But do you want to learn? If you develop applications, websites or anything else that is related to software, emphasise on this!
As you're likely not to apply for a senior position, who you are and what you can learn is much more important than what you already know. If you have projects (preferably open source), the company will be able to see that you actually like to program and that you're able to learn on your own.
Learning on the job does not mean that you will be taking courses, it just means that you will encounter problems and you are expected to be able to handle these problems. Research the problem yourself, but always ask others if you cannot find a solution within a reasonable timeframe.
You really have nothing to worry about.