I know it probably varied greatly between the years but I always imagined it as daily or nightly fights over Europe. However I realize that that pace might be unrealistic especially in the earlier stages before the US and UK built up their superior forces. I'mmainly curious about the allies but would appreciate insight into the axis side as well. Thanks in advance for any answers, this sub has already exposed me to many in depth concepts that I doubt I would have ever learned about otherwise.
Weather permitting, there was some level of bomber operations most days over Europe, or more accurately most nights in the early part of the war with both the RAF and Luftwaffe switching largely to night bombing by the end of 1940. RAF efforts were rather limited at first; "During the first two years of the war Bomber Command was small, ill equipped and ineffective", but by 1942, with Arthur 'Bomber' Harris in charge and heavy bombers such as the Avro Lancaster in service the strategic bombing campaign began in earnest, with the USAAF starting daylight operations in mid-1942.
Bombing the European Axis Powers, A Historical Digest of the Combined Bomber Offensive 1939–1945 by Richard G. Davis includes a CD with a spreadsheet of RAF and USAAF bomber operations, to really drill in to details. The nature and scale of missions varied widely, from a single aircraft dropping leaflets to the well publicised Thousand Bomber Raids and beyond; according to Davis' data the busiest day/night was 14th October 1944 with more than 3000 bombers involved in Operation Hurricane, plus around 400 Fifteenth Air Force sorties from Italy. To give a slightly broader idea of the frequency of raids there was only one day in October with no recorded missions (Oct 8th), on 18 of the 31 days there were over 1000 sorties.
In both the RAF and USAAF there was the idea of a combat tour, a number of missions (or number of hours) to fly after which the crew would rotate away from the front line, often acting as instructor in a training unit. Bomber Command's guidelines were after 30 sorties not exceeding 200 hours flying time, initially it was similar for Eighth Air Force with Commanding Generals having discretion to relieve personnel after 25 missions and 150 hours, but the policy varied depending on availability of replacements, overall loss rates etc. I'm not sure it's really possible to generalise the frequency of missions by squadron or crew over the whole war, and Davis' data isn't categorised by squadron, but operation records and diaries can give specific snapshots. A few examples:
A fascinating diary of a Canadian Lancaster pilot, with a list of his 30 operations ( http://www.lancasterdiary.net/operations.php ), June - September 1944
The National Archives hold RAF operations record books (ORBs), and have an example available to view from December 1943 of 101 Squadron who were flying Lancasters; they flew 6 operations that month on the 2nd, 3rd, 16th, 20th, 23rd and 29th.
The 306th Bomb Group Historical Association have many records in their archives including Mission Reports, showing e.g. reports from 78 missions in 1943.
I'm afraid I haven't got comparable detail for Luftwaffe operations or the Eastern Front, but very broadly the heaviest German bombing of Britain was the Blitz of late 1940/early 1941, with the bulk of forces then reallocated to the invasion of the Soviet Union. Strategic bombing was not a priority for the Luftwaffe, being primarily concerned with tactical support of the army, so though German attacks continued in various forms (hit-and-run raiders, attempted retaliatory raids such as the Baedecker Blitz and 'Baby Blitz' and eventually the V-1 flying bombs and V-2 rocket) it was never of the scale of the Allied offensive.