Bleeding gums indicate inflammation, inflammation of the gums are called gingivitis. Now, if gingivitis is concurrent with loss of supporting alveolar bone, then it is called periodontitis.
Anyone can get gingivitis as long as one does not brush his/her teeth for more than 10-20 days. (especially for dental students, Loe et al.1965) But not everyone gets periodontitis. This depends on your immune system's reaction to the source of inflammation, usually or most of the time, due to bacteria.
Now there has been lot of research on smoking and periodontitis, and it is considered a risk factor for periodontitis. But the major problems with these studies is that smokers also tended to have higher levels of plaque than non-smokers.
The most quoted paper on "smoking and periodontitis" is Bergstorm (Sweden 1986) and it claimed two things. First, it claimed that plaque accumulation was similar in smoker and non-smokers (meaning in the other studies, smoking was not the cause of more increased level of plaque, oral hygiene was: This is more of behavioral issue, not biological).
Secondly, more interestingly, it also claimed that smokers tended to have lower levels of bleeding. (The paper claimed that nicotine (or the tobacco smoke) causes vasoconstriction, which slowed or decreased blood flow to the site of inflammation.) This has an important effect, it decreases bleeding, but it also decreases immune response and healing. There are several other papers that back this theory: Smoking causes impaired healing in orthopedic surgery, plastic surgery, dental implant surgery, and all aspect of periodontal therapy including non-surgical treatments.
Now, that we got the backround out of the way,
so the reason why one bleeds after quitting tobacco smoke and starting on electronic vapor can be many fold. It could depend on personal oral hygiene care, it could be that bacterial level has increased, it could be that vasoconstriction effect of tobacco smoke is decreasing and your normal bleeding response is beginning to show (this is if another chemical was the major vasoconstrictor in the tobacco smoke, and now we restricted it/them), however if nicotine could still be the major vasoconstrictor and could be that your usage of the electronic cigarette based vapor has lower dose of nicotine than your former analog usage. <-- anything is all speculative.
So this is what I would suggest if you have bleeding gums: brush well, especially around your gum/tooth margin with a SOFT bristle, and floss. Use listerine, or any other OTC mouth rinse you prefer and keep biofilm plaque off your teeth and gums for 10-14 days. If you still have bleeding gum issue after that, you should find a periodontist (or a general dentist because you usually need a referral) and find out exactly why. It could be the initial stages of periodontitis.
hope that helps...