Just to make sure i am understand the RAW...
Bob grapples Pete with his normal CMB, and beats Pete's CMD initiating a grapple
Pete trys to break the grapple with his Normal CMB and fails
Bob maintains the grapple with a +5 to his CMB because Pete didn't break free right away, succeeds and gets to do one of the many things that you can do in a grapple with that same check
Pete trys to reverse the grapple with his normal CMB and succeeds and that is his standard action, just reversing the grapple
The 2 main points i am trying to clarify is the +5 to maintain a grapple, and that 1 check maintains and lets you take a action in the grapple
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That is pretty much it yes.
However to continue your exmaple if Bob then attempt to reverse the grapple again or break free, it isn't clear whether Bob still gets the +5 to his CMB:
"If your target does not break the grapple, you get a +5 circumstance bonus on grapple checks made against the same target in subsequent rounds."
Pete didn't break the grapple on his second turn, he reversed it instead, so according to a literal reading of the RAW Bob should get the +5, however I don't believe that is what was necessarily intended.
Also remember that apart from the initial check to start the grapple all subsequent CMB checks are against the opponent's CMD-2 (as both parties have the Grappled condition that imposes a -4 Dexterity penalty that equates to a -2 to all Dex related stats including CMD). Also that bonus applies to CMB if Bob or Pete have Agile Manouevres (or they are Tiny) and thus add Dex to CMB instead of Strength.
mmm i did miss that, thank you