First of all as Rob Whitaker and J R Holmes were nice enough to point out you do not get the bends moving from lower pressure to higher pressure too quickly. I was lumping oxygen toxicity and nitrogen narcosis into 'bends' because air pressure! Oopsie.
Assuming you do have a suit pressurized to less than an atmosphere (say half) going into a ship pressurized at one atmo is not going to inconvenience you terribly as the pressure change involved is not huge. Nitrogen narcosis is a concern at a couple of atmospheres' pressure at least. A half atmosphere would be the equivalent of half a martini to go by a popular rule of thumb (Note: you do not want your damage control drinking before the crisis. After ... )
I'd like to point out that air tanks are rated for how long they'll last at one atmosphere. Your standard spacesuit has tanks lasting six hours. If you enter a two atmosphere environment they last three hours. If you step out onto the surface of Venus (100 atmospheres) you're screwed!
Klaus Teufel brought up using skintight suits that use their own compression to simulate atmospheric pressure. I actually did a post on this waaaaay back. As Raymond McVay pointed out compression garments are less than comfortable to wear ('like a tourniquet at each joint") and you wind up wearing a spacesuit (with all the relief tubes and other hygiene related devices) errr inserted for your shift. Not fun.
Since I like dumping on any and all solutions presented (including my own!) let me point out these compression garment type suits take a while to get into so you're not going to want them for everyone to grab in the event of an emergency. They are also more or less tailored to the individual and cost a lot more than your standard suits
They also take a while to get into depending on how you construct them. They are harder to make and probably cost more. They could be worn under uniforms but they trade that streamlining for protection. You could throw Cloth/Reflec over them though for added protection.
A comfortable skintight sort of spacesuit or softsuit you can wear in standard pressure might be a few tech levels away. But since this is science fiction I'm going to include them and stat them.
Assuming you have a spacesuit and have some damage to control: what do you do? Rod Thompson was kind enough to share his (Wet) Navy experience with me:
" I have a lot of experience with wet navy shipboard damage control, but not with working in pressure suits. I would expect that in a catastrophic event the question isn't how fast can you suit up, but can you make it to the other side of a pressure tight bulkhead before the automated systems close all the doors?* The principles will be the same in any hostile environment. Can you contain the damage immediately?** No, then get the hell out of the compartment to a safer space. Contain the damage, evaluate all damaged areas, prioritize the work and repair. Keep monitoring any damage you aren't currently working on and reprioritize if your containment starts to fail. BTW couldn't you get in a suit at a standard pressure and then do your decompression within the suit, assuming it had the appropriate controls***?"
*Depends what kind of game is being run.
**Do you have a big enough patch? Do you have a big enough extinguisher? Of course if you need a patch and a fire is burning that's what we call a self correcting problem!
***Yes I believe you could get into a suit at standard pressure and then reduce the pressure gradually and exercise to decompress. Certainly with the the higher tech suits. Exercise in a suit will not be fun. But hey, life or death and all that.
Some stats on space suits and their use are coming up.