I didn't read every single post so this may be a re-post but I'll throw in my two cents.
As I saw someone mention, your league rules may have different scenarios that override this but regardless the secretary alone does not have the power to dismiss a bowler.
As a general rule, only a meeting of the board (consisting of all officers and in some cases all captains in your league) can make a decision on the dismissal of a bowler. If the majority rules that you should be removed from the league then you will not be allowed to bowl in that league.
As it pertains to USBC rules, they have no authority over any decision. Your league secretary can file a complaint with USBC which will initiate an investigation to your status as a "bowler in good standing". They basically check to see if you pay your dues, have you had an issue with this league or any other league before, have you cheated on scores etc. If the secretary's case against you does not hold, which in this case it would not, then it would be completely dismissed. As for dismissing you for a year, again this decision is up to the board. If you are kicked out of the current league it does not automatically dismiss you from a summer league or from returning the next year. For each season of this league the board will have to make the decisions on who is allowed into their league.
Bottom line, if he suspends you from the league without a quorum from the board then you can report him to USBC and his status as secretary will be removed and you can be re-instated to the league.
Your secretary is putting himself in a very bad position here, and to be honest, your President is not doing his/her job of trying to resolve the situation. Your next steps are to talk to the other members of the officers board, (President and Vice President) and plead your case to them. It's their responsibility to make sure that all officers are performing their jobs correctly and efficiently.