Hi guys, I'm looking for a bit of advice from a bass player's perspective.

I teach at the local music school. Predominantly guitar, because that's my instrument but I have 2 bass students at the moment too, and have had for about 4/5 months. The first young chap is 13 and has only been playing about 9 months but is coming along well. We just started looking at Rockschool's Grade 1 book and everything's fine at the moment.
The other lad is a bit older and I'm looking at Grade 4 with him. He's obviously more of an intermediate player. He's pretty comfortable getting around the instrument now with a good technique and sense of rhythm and everything else. So we've been doing a little scale/arpeggio work and improv with them - pentatonic 5 positions/major, minor, dom7 arps - because that knowledge was lacking. Have also just recently went over chords in a key and the concept of relative majors/minors and he seemed to pick that up quite well. His rhythm reading is also good, certainly beyond the (admittedly low) standard Rockschool ask for their exams. Reading pitch is something we haven't looked at yet, mainly due to my own apprehension as a treble clef-er. He has said he's familiar with it and it's absolutely something I'll be looking at soon.

SO, my questions are as thus:
As (hopefully experienced) bassists, is what I am teaching him appropriate? Is there any bass-specific concepts I should be going over with him at this stage that may have slipped my mind? Or any advice generally about learning and teaching bass at any level would be helpful.
Bass clef is definatly something to teach.

Chord structure and how it transposes to basslines by arpegio's and scales.
Improv over common chord porgressions can always help, II - V - I, I - IV - V etc.

Walking bass is definatly you could look into as well.

If they have any interest in jazz working on some standards seems like the obvious choice. Trying them out in different styles (straight, swing, bossa, ...), learning how to construct a bassline in each style, learning how to improvise a solo, learning to play the melody and the chords even if they're up to it.
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I am a self-taught bassist, and I can give some input based on what worked for me.

A little background - I am not a professional musician, but I am still a musician. Started as a child on piano with formal lessons. Learned saxophone next and again, with formal lessons. This became my primary instrument for many years - played in high school orchestra and jazz band, etc. Around the age of 13 I started playing bass - self taught - also play a little acoustic 6 string guitar. I studied music in college for 2 years before changing to a different major and the bass became my primary instrument - has been ever since - about 35 years total now (48 years old).

Having played both bass and 6 string guitar I can tell you, and this may seem obvious but it is sometimes overlooked, that bass requires more strength - strength in the fingers, wrists, forearms, etc. One of the best things anyone learning bass can do is repetitive exercises that build strength and dexterity. Some things I do every time I play, both as a warm-up and strength builder (by the way, I mostly play finger style - no picks and only moderate slapping):

- plucking hand only (fretting hand is at my side, not holding the neck), I use a metronome set to 120 BPM, and I play 16th notes on the open E string for 5 minutes non-stop. After a quick rest, I repeat for the other open strings, A, D, and G - 5 minutes each. This helps to build consistency between the plucking of strings, consistency in timing, and strength in plucking
- then with both hands, I begin doing patterns up and down the neck. Chromatic steps that progress up and down the neck for each string, patterns such as whole step and then half step, half step and whole step, up and down the neck on all strings, also moving between strings, arpeggios, pentatonic scales, major scales, minor scales - anything repetitive up and down the neck and on every string - for about 30 minutes non-stop. In addition to strength building for the fretting hand, this visually reinforces the position of each note to each fret, the patterns or shapes of scales, etc.
- once you can easily do the two items above, slide a small piece of rolled up cloth, small rope or something similar under the strings and push it up near the nut - kind of the opposite of a capo - it temporarily raises the strings and action, and makes it harder to fret each note - thereby building even more strength. I actually learned this trick by reading an interview with Bill Dickens - an amazing bass player - you case easily see the results by searching and watching him on YouTube

Another simple thing is to have your students play along with music they like. Give them an assignment at each lesson to learn the bass part of a song they enjoy, and have them play it for you during the next lesson. I honestly learned the most by playing along with songs. For example - I am a BIG Rush fan - Geddy Lee. By learning and playing his complex bass lines, I became a better player. Same thing with Chris Squire of Yes. I also learned pop, jazz, R&B and many other genres, which teaches a well-rounded technique - "walking bass" lines with jazz, slapping with some pop and R&B songs, blues and pentatonics with Rock. It also helps to develop their ear - learning perfect pitch (if they can) and relative pitch. The best part - it makes learning fun.

Sounds like you are already teaching them some of the other important things, reading music and bass clef, general theory. Not sure if my advice helps?
Yes, thanks! Both very helpful responses and advice I will definitely take on board. I have been looking at Scott Devine's lessons and getting some ideas from him, too. Always more to learn!