It is worth keeping them, turn them in on Sunday or Monday and even 6 or 7 will get you upto rank 4, then turn in just 1 weekly and you've got rank 5 on first character then it's even quicker on next 2 characters.
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I haven't actually gotten 2 characters to rank 5 before usually I just do the one and buy whichever gear I might want. It's usually very frustrating so I only put myself through it once
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Try just running your main for fun every day, keep your bounties then on Sunday or Monday if you've got the patience and time, hand in those bounties and try on the other 2, honestly I'm crap at PvP and can manage it on both my own pro and gfs.