Offer membership to raise money!
GitHub and similar sites make money by requiring people to host public projects if they're using the free service. So there's one option for fund-raising right away.
TypeKit is a subscription-based service that provides web fonts to subscribers. I wonder if you could make CircuitBee work the same way? i.e.: service is free if you just point people to the circuit here on the site (or embed a PNG/PDF), the full embedded browser would require an active subscription.
Alternately, stick up a PayPal donation link and see if you can gather enough donations in a year to buy a coffee :)
IMHO you should try to make money from day 1 so when you find you have to pay for hosting, you aren't going to catch people out by surprise.
You are absolutely right, as soon as we’re leaving the alpha stage we will have to find some ways of monetizing the site.
A small fee for enabling public embeds of circuits might be good, but it really depends on the users and whether or not we’re providing enough value.
We have been planning some advanced features which perhaps would fall under a ‘pro’ account. We’ll have to see how this goes in the days ahead.
Christopher Cook commented
Having operated several popular websites the paid membership route is difficult and high maintenance, suggest you relying on ads within site pages instead, not great revenue but good if you get enough traffic.