Make or buy yourself some flash cards for bass clef notes. Begin with a very small subset of cards -- choose several that you can identify reliably, such as middle C. If you have, say, 3 easy cards and 2 slightly harder cards, that's a good combination. On the back of the card, write the name of the note. Now shuffle and quiz yourself. Say the names of the notes out loud in a normal voice -- don't just think it or mumble it. You can use or invent your own memory trick such as "All Cows Eat Grass" (for the spaces), as shown at http://www.piano-lessons-made-simple.com/bass-clef-notes.html. Or you can draw a picture based on the way a certain note looks. Anything that helps you get good results with your quiz will help.
Do this shuffling and quizzing for a short amount of time frequently. I have seen a model of vocabulary memorization that said that a new vocabulary item needed to get loaded into, and retrieved from, the short-term memory seven times before the item would make it into the long-term memory. (As I get older, it seems to be more challenging.)
Also, sit down at the piano and quiz yourself with the shuffled cards by playing the note on the card. For this, you may find it helpful to draw a picture of the white and black keys, and shade in the note in question.
You can also try playing Concentration with notes that match in name between treble clef and bass clef.
When you are very comfortable with this first small set of note cards, add one or two new ones. They don't have to be neighbors. You could start with, for example, the notes of the C major triad.
Buy a cheap mp3 player, such as a Sansa Clip, that has a voice record feature. Record yourself playing the right-hand part of a not-too-challenging piece, nice and slow. Create a click-track by plugging your headphones or earbuds into an electronic metronome, and listening to this metronome while you play and record your right hand.
Now, play back the recording, while playing only the left hand of your piece. You will have the headphones plugged into the mp3 player at this point.
This will only work if you keep a steady beat with your click track when you record the right hand.
Remember, nice and slow. Slow and steady wins the race!
You might enjoy working with a beginner's music theory exercise book. They have all levels -- just browse at your music shop and pick out something that seems doable but not too easy for you.
One more thing -- don't neglect your ear. Try to play some simple tunes with your left hand, entirely by ear, so as to get comfortable with that part of the piano's range, and so as to make the connection between the intention coming from your brain, and the sounds that your ear hears when you strike the keys.
P.S. (because I'm not allowed to comment) I like Reim Time's idea, and I want to reassure you about it because of your comment. Think about what it was like when you were little, and learning to read. It was a dialectical process, with both reading (which is a relatively passive activity) and writing (which is more active) going on. We just need to engage the brain in lots of different ways.
Bottom line, try lots of different activities and approaches. As your confidence grows, the positive effects will snowball, because any anxiety that may have been slowing down your learning process will stop getting in the way.
Happy music making!