It would take a lot for me to burn a bridge, and there's so much more to it than salary.
But for the right opportunity I would certainly move on even during tax season. Lots of factors to consider, first and foremost WHAT is the job description. Operations Manager couldn't be more vague, in fact its rarely used for an accounting or finance position at all. Is it something you truly could see yourself doing, is it a pretty big stretch for your skill set and if so will there be ample training and mentoring. Big salary boost isn't worth a job that makes you positively miserable.
Once the job description is known, is the salary being offered comparable to similar positions in the same area. I don't care if it doubles your current salary, if its not in line with the same job in the same sized company I'd walk away from it. Also to be considered are the benefits and hours. Again it doesn't matter if the salary is substantially greater if your current employer is paying 80% of your insurance and this place pays 50% or less.
If it all worked out your new employer may consider letting you work reduced days/hours while you're getting up to speed and helping your current employer through tax season, or offer to stay on part time to help through tax season. They may not take you up on it but you're less likely to have burnt a bridge.
I guess my point is I would walk away from a position and risk burning bridges even for a CUT in salary if it was the best opportunity for me. On the other hand there are some jobs that aren't worth a HUGE increase in Salary for any reason.
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Massachusetts CPA (non reporting) since 3/12.