Stomp box?

No sooner do you post a question...
I guess something like the Behringer MX400 will do the merging, which I gather real musicians call mixing.
That leaves the foot drum / Stomp box part of my question.
Opinions there very much appreciated.

From the ugly who has no sense of time.  Pick up a cheap casio or yahama keyboard   Many of the keyboards have beats built right into them.  Then pickup the beats with a set of headphones (use only one ear).  It might be possible to use your amp as a monitor, and the keyboard as mixing board. 

I would try a metronome you can adjust the tempo to match what you are trying to play

i was going to suggest a little behringer line mixer.  i have one of the $20 4ch jobbers....  smaller than an FX pedal too.

+1 on the metronome

Actually, I _am_ using a metronome. Maybe I haven't been clear enough about what I'm doing.
I am playing a song with mostly sixteenths (TOP - Soul with a Capital S etc.), and I have the metronome clicking the base beat (~120).
I know which note I need to be playing on the beat, and to enforce that, I tap my foot on the beat which is then a different rythm to what my fingers are doing... Any decent bass player should be able to do that, right?
The thing is... The metronome goes click, my bass goes boom boom boom (i wish), and my foot goes... Nothing. My shed is carpetted, and short of donning clogs, my foot tapping is just never going to be audible. Hence, it is hard to tell whether my foot is exactly on the beat, or only just about.
A stompbox would make the foot part of the signal, and it would become very clear whether I've nailed the beat as well as the song.
Am I making any sense?

Sounds rubbing the belly and tapping the head.  Difficult at first but achievable for most.  (I am timing challenged).  Get yourself a 12x12 or 16x16 tile to tap your foot on, it will be louder.

I am under the impression that you are also recording your self. 

Don't be surprised to find that you either consistently lead or lag with the foot.  The key there, is consistency. 

My kid has a 4 channel recorder (phillips tape) and also records on a MAC. 
My hat is off to you because you are working with 16th notes.  Even eighth notes kill me. 
You are trying to improve, and with the sense that you trying to improve yourself will result in you being a better lowdown ugly. 

you could always buy a cheap hi-hat stand/cymbal and use that.....

How do mixers like bass input? Can I just plug my bass straight into a mixer, e.g. one of the 1/4 inputs of a Behringer Xenyx 502?
The tile is a good idea, I'll give that a try... I usually play sitting down, and I find that if I have to tap my foot too hard, my leg moves and my bass is all over the place - those 16ths are hard enough when the darned thing is immobile!

Interesting idea with the cymbal, but I think that would out-noise my bass.
Thanks for your input + encouragement!

a mixer should have no problem with your bass....

Jackie is correct. 
The high-hat is also a good idea (borrow one if you can). 

There is a range of mixers out there. some accept multiple types of inputs such as XLR, balanced jacks. Read the specs.   

I _have_ read the specs of several mixers out there, before asking here. But I never was much good with the technical side of electronics.
The thing is, AFAIK, the output of the bass is not line in (it's high impedance?), but it seems it might work anyway. I'll give it a go.
Incidentally, I think I managed to motivate my 6-year-old to help me construct the stompbox, so that should be fun.
He'll have a 34-year lead on me concerning piezo pickup experience. We'll both be starting from zero.

With an older learner side by side, the youngster is not starting out from zero.  Because he has you to help, he will learn much quicker.  There are three rules to teaching kids, 1, make it fun, 2.  make it fun 3. make it fun. 

We've done a couple of practice sessions now, and I must say, it is _fun_! .-)
Like you say, it has to be fun.
I figured we'd skip the chapter on music theory, he can always pick that up if he feels the urge one day...
And I must say, so far, _he's_ giving _me_ lessons about dedication and motivation.

Your kid will learn theory by reverse osmosis.  For example, if he's playing twang box, you'll show him the G chord, maybe some tab, and possibly some staff (treble or possibly bass).  When you tell him he's playing a G, a B, a D, etc, you can tell him about thirds and fifths.  thats theory.  when you show him the notes on the staffs thats theory. 
For example, when you capo the twang box, and it allows you to play a simpler chord, thats theory application. 
Playing with your kid is more fun than playing by yourself.  Thats why we jam. 
P.S. don't be surprised when he gets better than you, but who cares, the music lives on.

It's lots of fun to have the little one spontaneously go off on a solo trip.
I catch myself almost telling him to get back to the exercise, but then I just let him fly - it's all practice, and it's great fun to hear him play stuff that's not on the page!
The harmonica is also a great reason to learn to read treble clef, so far, I only did that to transpose stuff into the ugly register...
And you're right, playing automatically teaches you theory, you just don't know it by that name.