Cost of lending out a child's bike?
The marginal cost of cycling is extremely low (i.e. the cost for an extra bit of use), especially as kids' lessons are going to be light use (I doubt they're hurtling off kerbs, for example). Kids' bikes are also heavily built in proportion to their riders, who are weak compared to adult riders, while the chain (for example) is unchanged.

Depreciation of bikes has little to do with distance travelled and more to do with age (unaffected by the loan) and apparent condition (e.g. rust - how are they stored? How often are they dropped on painted parts?).

If the bikes are being serviced once a year anyway, that's probably enough for some extra riding, though they may want a safety/basic check after being transported between sites (have the brakes been knocked, is there air in the tyres...?).

Ultimately this is a form of business decision (though I dislike the term in this context). It's highly unlikely for the extra wear to shorten the life of non-consumable parts, so if you covered your consumables costs (with a possible allowance for extra wear) you should be fine. Accident damage is another matter (also theft etc.). I suggest you enquire about insurance but probably choose to self insure. 

You should talk to the LBS volunteers to get an idea of whether they think they'll need to do more, and whether they'd be happy to do so on the same terms.

So to actually estimate what it might cost, I'd start from an average consumables cost per bike per year from your records. This is for a month's use, so I'd try to recoup that per month lent out. This is almost certainly more than enough alone as rust and perishing rubber are a function of time, but if the number you get from that seems low in the context of the market (sorry!), a safety factor wouldn't be a bad idea. Obviously if you do end up with (extra) insurance costs you'd factor this in, and you'd gauge interest in advance to know how to share that between renters.