Below are some of the newspaper cuttings and reports that show team fixtures and give details. Where the team played is also not yet clear. As a guess, I would think that it was at the cricket field in Kettering Road but, hopefully, this will be made clearer if more information is forthcoming. Judging from the limited information available, the team wasn't particularly successful, which may account for the fact that nothing has been found after 1903 ... yet.
The fixture list below from the Bedfordshire Times & Independent dated 9th November 1900 and the smaller clipping is from the same newspaper dated 7th December 1900.

On 24th January 1902, the Bedfordshire Times reported on a match at Bedford against Burton Latimer: "The return match was played in the Park on Saturday, Bedford were very weak owing to the absence of their usual backs and halves but in the first five minutes of the game Bedford had rushed the ball down to the visitor's goal and scored. During the first half of the game the play was mostly confined to the Burton Latimer goal, and although the visitors tried an occasional rush, they were only allowed to score once. After half-time neither side seemed to be able to score, though Bedford were continually in the visitor's circle. When the whistle blew Bedford were the winners by 4 goals to 1". The names of the Bedford team are listed but unfortunately not their visitors'.

Later that year the Bedfordshire Times & Independent 21st November 1902 reported:

BEDFORD V BURTON LATIMER
On Saturday the Bedford team travelled to Burton Latimer to play the local club. For the first quarter of an hour, the Bedford forwards found fielding rendered difficult, and passes practically impossible, by the bad state of the end. The first goal was scored by Burton Latimer by Coles. The visitors then pulled themselves together, and after several ineffectual attacks, equalised. The ball bounding off the goal-keeper’s pads from a shot by Walford, and being netted by Rolfe. The latter also scored shortly after the call of half-time, by driving a long-hop pass by Field straight through the posts from the bounce. The greater part of the second half consisted of a series of assaults on the Burton Latimer goal, and at length, a few seconds before the final whistle blew, Walford added a third goal by a stinging shot, which the goalkeeper had little chance of stopping. For the home side, Westley and S. Whitney at back, Arthur Buckby at half, and Clark among the forwards were prominent. For Bedford (who lacked the services of F. Thornhill, Holmested, and P.A. Baumgartner), Nixon made a promising debut on the outside right, and Van Cuylenburg was again cool and resourceful in goal, while Chambers and Wilmot at half-back, and Wright at inside-right, also put in very hard work.

Arthur Buckby		S. Whitney

The Kettering Leader reported on a match between Burton and Finedon on 13 March 1903:

"Burton Latimer played Finedon on Saturday in very rough weather, and after a somewhat rambling game the home team managed to secure victory by three goals to two. Burton won the toss and started with the wind in their favour and were quickley at work, Downing getting close in and scoring with a fast shot. Play was transferred to the other end, the defence being severely taxed, and after a long scramble round the home goal, F. Elson scored for the visitors. However, Popham restored the lead for Burton. In the second half Finedon equalised through Roberts, before Downing got the winner for the home side."

The Buckingham Advertiser and North Bucks Free Press 7th November 1903 included the report below