First, while it may actually be true that your lack of success was due to a lack of strength (though, my guess is that your technique was also quite poor and that it was this, not your lack of strength that was primarily to blame), your focus/attitude towards training seems to be the most limiting factor you have currently working against you. This may be at least partly your instructor's fault was well though.
I tend to agree with Zecarlo that this does not sound like a good training facility, or at least not a good fit for yourself. Realize that not all coaches, even good/successful ones, are good at appropriating what they teach to accommodate different types of students. For instance if someone is a very strong, hard nosed wrestler, they may be very good at training other people who fit that same mold and both coach and athlete might wind up being quite successful. But that same coach might have absolutely no idea how to train a weak, finesse oriented Jiu-Jitsu fighter or striker. And no matter how hard he/she tries to jam that square peg into a round hole (ok, I fully expect some sort of drunken motel sex comment from Robert from that one LOL), he will never make that small, weak finesse fighter into the hard nosed big strong bull that he is accustomed to and good at coaching.
What you need to find is a coach or training facility that can appropriate the skills to all types of people, or at least one who shares your basic archetype (unathletic, relatively weak, finesse based strategy vs physical based strategy). That training facility will also most likely have a different "feel" to the classes which will be more in line with your personality (focus on learning rather than "winning", working with your partner to both get better rather than against them to "beat them", focus on technique, timing, and precision rather than brute force, etc...).
Now, it's also possible that the problem is entirely you and by simply changing your attitude towards training and perhaps approaching the instructor about the problems you are having, speaking up in class and asking for help or clarification if something isn't working/you aren't getting it will solve the problem. But seeing as you said you already did several privates, I tend to think otherwise.
Finally, as far as strength and conditioning work goes...
First, nothing beats specificity. If you are having trouble with bridging, then either have a training partner lay on you or get a sandbag/heavy bag/grappling dummy and practice bridging both straight forwards as well as to both sides. Once you can do 10 reps in all 3 directions (without resting) try doing an actual bridge and roll, then practice passing their guard, mount them and have them repeat the process.
You can change the mount escape/guard pass each time (or cycle through a few that you both like, they don't have to be the same ones as your partner either) if you want or just really drill the heck out of one escape and one pass. Then you can increase resistance (you/your partner can actually somewhat defend the escape/pass enough that you have to improve your timing, set-up, or technique to make it work) once you can both perform your techniques with ease against no resistance. You want to add resistance slowly though (since you technically still want your partner to be successful most of the time) lest you degrade back into full on live rolling and start trying to rely solely on brute force and throw technique out the window.
This is a very "simple" drill/concept that has nearly unlimited potential for variation and application. And since you are actually practicing skills that will directly translate to grappling, the carry over to actual grappling will be higher than pretty much anything else that you can do.
The second option would be to perform basic resistance training or strongman/conditioning types of workouts with a mix of non traditional (rocks/stones, water jugs, kegs, anvils, water bags, tree trunks/logs, battling ropes, sledgehammers, partners, etc...) and traditional (barbells, Dumbbells [preferrably thick handled], kettle bells, club bells, etc...) equipment. This won't carry over to your grappling as much as sport specific drilling like what I described above, but as far as strength and even more so conditioning go, this type of workout will do a great job of improving your LAT (Lactic Acid Threshold), build a lot of grip strength (which is very helpful for grappling), and more closely resemble the type of strength that you will need when grappling than traditional resistance training programs.
If none of those are an option you can pick a traditional resistance training program that is geared towards performance (WS4SB and 5/3/1 are both popular programs that have good track records).
Hope this helps.