Oxford Boating before 1820

Almost certainly the bumping races started sometime before 1815 when we have the record of the first head of the river.

The Royal River (1885) -

The great deed of the new undergraduates was the discovery of the river.  In the early years of the (19th) century it was still only a place for fishing in;  occasionally a heavy tub was rowed down to Nuneham.  Bell-ringing had gone out as an exercise; cricket was the game of one exclusive club.  The nearest approach to a healthy rivalry between colleges was a competition between New College and All Souls in making negus.
[ A drink made from 2 parts Port, 1 part Claret, 1 part Burgundy, 1 part Brandy, 2 parts water, Lemon slices, nutmeg, 1 teaspoon Sugar. Served hot. ]
New College won by putting in no water ...

G V Cox, writing in 1860 about 1805 -

Boating had not yet become a systematic pursuit in Oxford. Men went down to Nuneham for occasional parties in six-oared boats (eight-oars were then unknown), but these boats (such as now would be laughed at for tubs) belonged to the boat people; the crew was a mixed crew got up for the day, and the dresses worn anything but uniform. I belonged to a crew of five, the first, I think, distinguished by a peculiar (and what would now be thought a ridiculous) dress, viz. a green cap, with a jacket and trousers of nankeen!

The environs of Oxford are very pleasing and picturesque, especially when viewed from the Isis, down which river conveyances may at all times be procured in small and neatly painted boats as far as Iffley Paper-Mills. This is a pleasure in which the students are fond of indulging.

1811: from ' A History of Oxford Rowing -

The River, 1811

The only other record of this time is a picture of the river from the towing-path opposite where the barges now stand [ ie opposite Christchurch Meadow ]. The foreground is foreshortened to enable the artist to throw up the buildings of Christchurch, but it is with the river itself that we are interested. It will be seen that there are no barges, no boats, even, in sight, except the primitive one to the right, no wall on the meadow side, and of course no railings. Such boats as there were, were kept at Folly Bridge, at the Boat House Tavern near the lock.
[ What is now the main channel at Folly Bridge was then a weir, and the LEFT bank channel the other side of Salter's was then the lock. ]
And here, just where our interest begins, the records fail us ...

1815: HEAD OF THE RIVER - Brasenose College
It is probable the only other competitor was Jesus College. Of course what the competition was nobody actually knows since there are no known records - however the implication of the earliest accounts (see 1817 below) is that this was a bumps

The Napoleonic Wars came to an end in 1815.
Enthusiasm for all things naval (except paying for the navy) was at its height. When the navy was drastically downsized many ships were sold off - and with them their ships boats - which included many gigs which were typical of the boats first used in rowing at Oxford.
That rowing could be a sport had been established in London in the previous century - what changed at this point was who participated. Up to this moment it had been watermen who rowed and gentlemen who bet on the results. Now for the first time University students took up the sport. ]

from Oxford by James Morris writing in 1953 -

- because the Thames at Oxford is both narrow and sinuous, a special kind of rowing race was long ago devised for the University.
It began, we are told, when oarsmen who had pottered down to Sandford for an evening drink started for home at different times, and made a custom of trying to catch each other up: and it has developed into a elaborate system of competitive rowing, in which college crews start at equal intervals and try to bump the one in front - thus taking its place in the next race.
A kind of ladder is formed, and the crew that bumps its way to the top of it, in a week of daily racing, becomes Head of the River, celebrates with a college binge, and chalks it insignia proudly on the quadrangle wall.
There are two such annual regatta weeks, for different standards of crews, but the big one is Eights Week at the end of May.

1816: HEAD OF THE RIVER - Brasenose College
1817: HEAD OF THE RIVER - Christchurch College
Christchurch drawing its crew from the two boating schools of Eton and Westminster. Brasenose and Jesus about this time raced each other in fours as well as eights, whilst a third four was owned privately by De Ros of Christchurch.

1817: Hall's Boathouse Tavern (near Folly Bridge) - showing an eight - from "OXFORD ROWING, A History of Boat-Racing at Oxford from the Earliest Times", by W E Sherwood, 1900 -

1817: Hall's Boathouse Tavern - showing an eight.
Drawn by G M Musgrove of Brasenose and therefore probably the Brasenose Eight, one of the first two in Oxford

It was the custom with these early eights to row down to Sandford, and then return together to Iffley Lock. The boats were large ones, with a gang-plank running across the seats down the middle of the boat.
When the lock gates opened, the stroke of the head boat, who was standing in the bows with a boat-hook, ran down the boat, either along the plank or along the side, and pushed her out of the lock as quickly as possible, immediately taking his seat and rowing. The first boat was followed as quickly as possible by the second, and that by the third, and thus the race was started.