Yuan Shao was at war with Gongsun Zan till the spring of 199 after a long campaign and final siege of the fortress complex at Yijing that was finally breached by tunnels collapsing the walls. Until the fall of his main rival, despite deteriorating relations between Yuan Shao and Cao Cao, former friends and Yuan Shao former patron, and provocations for some time, Yuan Shao left the border of the Yellow River alone.
Yuan Shao never seems to have been a figure keen on fighting on more than one front, though in the early years he had fought joint campaigns with Cao Cao to help shield his south against likes of Yuan Shu, Yuan Shao generally secured flanks via treaties then pushed against one major foe (Gongsun Zan then Black Mountain Bandits of Taishan then Gongsun Zan again). So till the final major threat on Shao's side of the Yellow River was defeated (though some local powers remained), Yuan Shao was unlikely to open up a major second front against his former ally.
It wasn't till the spring of next year that Yuan Shao's army of disputed size crossed the Yellow River so what went on between then? First a caveat. We don't have sources from Yuan Shao's camp, much of the narrative of Guandu has been built by Wei for whom this was Cao Cao's iconic victory and where lots of "compare and contrast" was done with Cao Cao and Yuan Shao with Yuan Shao portrayed in a negative way to enhance Cao Cao as a leader while we also have gaps where we simply don't have Yuan Shao's side of events.
Some of the delays would have been moving army back from the very northern edges of Yijian back to Ji, rebuilding it after a long campaign and building up the supplies for another campaign. Whether one goes with the traditional massive overwhelming army or De Crespigny's throwing everything together in a desperate strike to turn things around, that sort of army takes time to organize and gather.
Even after the delay, some in Yuan Shao's camp according to the Xiàn-dì Zhuàn still felt it wasn't time with Ju Shou and Tian Feng arguing against the campaign at that time and then a more defensive approach "The armies have gone out for successive years, the common people are weary and exhausted, the granaries without stores, taxation and conscription abundant, and these are the state’s extreme worries. It is appropriate to first send envoy to offer spoils to Heaven’s Son, attend to farming and release the people; if this cannot be communicated, then memorialize that Cáo is blocking our road to the Ruler, and afterward advanced to garrison Líyáng, gradually encamp the Hé’s south, increase building of boats, mend and repair weapons, separately send elite cavalry, to plunder their borders, to cause the other to be unable to be at ease, and we will obtain leisure. Within three years, the matter can be settled.”
There were personal issues to deal with. Yuan Tan needed to be summoned from Qing, star general Qu Yi was executed as he became too insubordinate to keep under control, his chief adviser Ju Shou was demoted and two-thirds of his command reassigned as frictions within his camp (the heir dispute perhaps not helped) had to dealt with. Diplomatic efforts were prepared, Chen Lin's famous proclamation, Zhang Xiu and Li Tong on Cao Cao's border were both contacted to see if they would ally with Yuan Shao, efforts made to encourage Liu Biao to attack, wooing the Wuhuan to keep them onside while Yuan Shao's camp is said to have had contact with many in Cao Cao's ranks. If there were administrative and internal matters that delayed things, we do not know
There were events from the outside. The Qing army under Yuan Tan was first needed to try (and fail) to reach Yuan Shu attempts to join his half-brother then Cao Cao sent Zang Ba to go onto the attack in Qing. While Governor Yuan Tan as Shao's eldest son and famed general joined the main army this may have caused some changes in plans as to how many troops could be spared from Qing. Yuan Shao would also have had to consider how many troops to leave in places like Bing and You where he didn't have full control over the provinces
There was talk of Yuan Shao aiding Liu Bei's revolt in Xu and Yuan Shao is accused of failing to intervene due to one of his sons being ill. However, the raids of Yu Jin and Yue Jin destroying several of Yuan Shao's forward camps and that Liu Bei's position collapsed quicker than expected might be more relevant as to why Yuan Shao's army didn't move.
In short, Yuan Shao had events to respond to, an army to build up for the big clash after a long camapign, one of his provinces under attack, diplomatic efforts to make. Even when he did attack, some of his inner circle felt he should wait a while as his side needed more time
Hope that helps
Edit: Forgot sources
Yuan Shao's SGZ and Cao Cao's SGZ by Chen Shou, translated by Yang Zhengyuan
The ZZTJ by Sima Guang translated by Rafe De Crespigny
Imperial Warlord: A Biography of Cao Cao 155-220 AD by Rafe De Crespigny