Holes.....
Worse, Antennae ...
]The likelihood of the other side just guessing the right frequency to take out Bubbles is as close to zero as you can get.
That's not how it works - EMP's are
pulse weapons. 'Pulse' implies 'broadband signal', always. No need to "guess the frequencies" when your signal covers pretty much
the entire accessible spectrum ...For illustration: The common approximation for a pulse is a (normalized) Gaussian f(t)=A/Sqrt[2*pi*sigma]*Exp[-1/2*(t/sigma)^2] with A the intensity and sigma the pulse-width, and it's Fourier-transform - i.e. the spectrum of the pulse - is ... again a
Gaussian Exp[omega]=A*Exp[-1/2*(t*sigma)^2], with the inverse width 1/sigma!
(In the math-prep courses in my Uni, I'd let 1st-semester Students make that calculation)
So bandwidth of the pulse goes roughly as the inverse of it's duration.
Or the weapon scans the frequency spectrum, and the pulse has plenty of harmonics so it covers multiple octaves. The range to be scanned could be inferred from the current state of general technology. A bigger concern is focussing the weapon to get sufficient intensity without taking out the user's own tech (even if not AI soldiers, they are hardly likely to be computer-free).
IMO, shielding Bubbles wouldn't be as hard as shielding static facilities, that have external high-wattage cabling from power-sources leading into them.
An EMP weapon would most likely not be a fission weapon, rather smth. like a pulsed microwave resonator - Nobody's going to detonate a nuke in LEO to take out an infantry platoon. A microwave pulse would mean somthing in the .3 - 300 GhZ, or 1mm-1m wavelength. Passive shielding could be achieved with a Farday-cage (of 'sufficient' thickness - I admit I have little idea what 'sufficient' would be) that has no aperture smaller than the wavelength of the incoming signal.
Covering Bubbles in a copper-mesh with holes smaller than 1mm would be the easy part - it could even cover her eyes, since EM-radiation in the visual range has wavelengths of several hundred nanometers (same as you can easily see through fly-gratings). Even a
"Milanese plate EMP armor" wouldn't pose appreciable restrictions on Bubbles' mobility - humans figured out how to cover the human form in hardened steel with minimum restrictions on mobility in the 15th Century AD (If you search a bit on Youtube, there's a guy doing
backflips in full plate armour, it's around 15-20kg).
AFAICS, The trickiest part would be any antennae she uses to scan the EM spectrum. Antennae are ... well, they kinda work at opposites to shielding, obviously. My ad-hoc idea would be to place the complete transceivers & A/D-converters outside the shielding, and lead the digitized signals through the mesh - no problem to fabricate shielded wiring thinner than 1mm.
Methinks the hard part would then be to isolate those leads from her insides, if necessary, or design the leads such that they burn through on their own in case of a current surge.