Well, the OP says "British and French bombers in Turkey, Syria, Iran, and Iraq". Syria and Iraq are French/British territories, so there's no issue there. Iran and Turkey are more interesting though. They must have agreed to accept the air bases, because the bases could only have been supplied with their acquiescence, and no invasion or even protest is mentioned. I have no idea why they would act like this, given that Soviet retribution would come straight at them. Turkey was sufficiently powerful to resist credibly, and while Iran wasn't, it was quite friendly with Germany in the 1930s. So I can only presume that Britain and France made them an offer they couldn't refuse. 
(My understanding of Pike is that it would have been launched from Syria and Iraq only, so this problem wouldn't have arisen. But that doesn't end up with Soviet armies charging into Turkey and Iran as easily, so it may be required for the story.)
(My understanding of Pike is that it would have been launched from Syria and Iraq only, so this problem wouldn't have arisen. But that doesn't end up with Soviet armies charging into Turkey and Iran as easily, so it may be required for the story.)
