There are plenty of photos of rocket tests and launches in atmosphere, and in these the exhaust plume tends to be a long thin flame.
Is this true for when rocket engines operate in a vacuum? My guess would be that they would be more sort of 'bulb' shaped or similar as the gasses rapidly expand in a vacuum, however I couldn't find any images to prove/disprove this.
Do rocket engines operating in vacuum not produce as much light and are therefore harder to photograph?
Sorry, no bulb-shaped exhaust plume, at least not in true vacuum. But you might see something similar to an incandescent light bulb shaped exhaust plume at high altitudes that first stages reach, up to about 135 km high (exact altitude depends on launch vehicle and its ascent profile) above sea-level where there is still some, albeit tenuous atmospheric pressure but the first stage is at separation still about three times lower than the orbital altitude of the International Space Station. And / or due to multiple engines geometry. SpaceX Falcon 9 first stage might be particularly good for such exhaust plume geometry due to its nine engines in octaweb layout with one central engine and remaining eight in a circle around it. Observe this video of DSCOVR (Deep Space Climate Observatory) launch atop Falcon 9 close to first stage separation:
But you're right, expansion rate of exhaust plume and with it its geometry are substantially different in atmosphere and in vacuum. Actually, even in atmosphere, with increase in altitude during first stage ascent and drop of atmospheric pressure this geometry will change;
During early ascent in high density atmosphere, exhaust plume that exits rocket engine nozzle is at lower pressure than its surrounding atmospheric pressure and it compresses it into a long and narrow jet. It also interacts heavily with surrounding atmosphere due to high exhaust velocity and temperature and forms a pronounced exhaust boundary layer where it ionizes surrounding air. This forms plume eddies that might, depending on nozzle ratio, form shock diamonds or shock disks where increased pressure plume layers intersect each other and a combination of higher and lower plume pressure and density gives it that distinct appearance. But initially, the plume will remain coherent and downstream of it, this also results in contrail or a vapor trail as the ionized air forming due to acoustic shock (supersonic exhaust velocity) and temperature difference draws in more atmospheric moisture that evaporates or even disassociates on contact with high temperature exhaust products. Rockets whose main engine exhaust product is water (such as STS Space Shuttle launch vehicle that used cryogenic liquid Hydrogen and Oxygen, or LH2/LOX for short) will of course produce much more vapor. So much vapor that it's been reported that noctilucent clouds formed sometimes even several days after an STS launch.
Soon after, as the vehicle builds up on speed and altitude, atmospheric pressure starts dropping and exhaust plume of first stage engines starts expanding. At a certain point, atmospheric pressure is exactly equal to exhaust pressure and exhaust plume is exactly the width of the rocket engine's nozzle. This is the so-called optimum altitude, or where first stage engines reach highest highest thrust coefficient. As the rocket climbs higher, ambient pressure drops further still, doesn't match exhaust pressure and exhaust plume starts expanding over the nozzle ratio:
Plume (a) over-expansion, (b) ideal-expansion, and (c) under-expansion in a bell nozzle during flight. Credit: Rocketdyne, 1999
So how much plume expands depends on the pressure difference between exhaust products and their environment. In vacuum however, where atmospheric pressure is nonexistent or near-nonexistent such as near-vacuum at LEO (Low Earth Orbit) altitudes where air density is so low it doesn't even behave as ideal gas any more, there's nothing in the environment to confine exhaust plume any more. It expands much more rapidly and loses density without any pinch effect and the boundary layer doesn't form either.
It looks a bit like a wide open reflector light shining through a slightly humid air in otherwise complete darkness. Depending on propellants used, heavier exhaust products might be somewhat more visible than lighter ones because they retain higher temperature for longer without losing it to radiation and thus produce more light for longer through black-body radiation. And there might be slight evaporation / ablation of nozzle materials creating more orange exhaust layer close to the nozzle for same reason. But since upper stages use as light exhaust products as possible (they achieve higher exhaust velocity which matters more than their mass due to the nature of kinetic energy $\begin{smallmatrix} \frac{1}{2}mv^2 \end{smallmatrix}$ increasing with a square root of velocity), and higher rocket's velocity additionally reducing exhaust density, visibility of exhaust plumes of upper stages indeed won't be great.
For a bit more on exhaust plume physics, both at sea-level and high altitudes, I'd recommend Col. Michael Heil's article on Rocket Testing at AEDC (Arnold Engineering Development Complex) that includes additional images and much better explanations than mine.
Why, they look like this :) Here's an image of 3 rocket engines firing simultaneously on the Orbiter. (up, right, and aft firing RCS jets)
Nota bene: the sorta-rectangular object just above the right-firing jet is a reflection in the window through which the image is being taken.
Since this question was posted, plenty of exhaust plumes have been filmed from the ground giving a nice impression of the long term expansion behavior.
So, no, I wouldn't call it bulb shaped, but yes, the exhaust expands in vacuum. It is most clearly visible when the launch takes place shortly after sunset or shortly before sunrise when the sky is mostly dark while the plume is illuminated by sunlight.
