Canadian Klimkait won -57kg gold at the long-awaited Grand Slam after Bilodid took -52kg bronze and Russia dominated the men's classes.
Jessica Klimkait was the star of the show on Day 1 of the Budapest Grand Slam in Hungary as judo made its competitive return after the start of the Covid pandemic.
The 23-year-old won all four of her bouts by ippon to take gold at -57kg, the weight class in which her fellow Canadian Crista Deguchi is the reigning world champion.
Daria Bilodid moved up a weight to -52kg and was defeated by Romania's former European champion Andreea Chitu in the third round.
That was the Ukrainian's first loss since March last year, but she went on to take bronze with France's Amandine Buchard emerging victorious in the event which was closed to the public.
In Bilodid's absence, Kosova's Distria Krasniqi beat Olympic gold medallist Paula Pareto to take the minimum weight title.
Both men's competitions culminated in all-Russia finals with Yago Abuladze and Abdula Abdulzhalilov scoring respective victories at -60kg and -66kg.
Daria Bilodid was one of the stars of the event but the Ukrainian, who turned 20 a fortnight ago, had opted to compete at -52kg instead of the -48kg class in which she is the two-time reigning world champion.
She was no match for Andreaa Chitu in the third round, the three-time World Championship medallist bullying her on the deck to score a wazari with a minute to go just after the young sensation had picked up a shido penalty.
Bilodid went into the repechage, beating Azerbaijan's Gultaj Mammadaliyeva before winning bronze with victory over Swiss Evelyne Tschopp.
She finished the contest in style with a kosoto-gake throw for ippon, but looked disappointed as she received a kiss from mother and trainer Svetlana Kuznetsova.
Amandine Buchard was seeded to meet Bilodid in the final and the Frenchwoman kept her side of the bargain before defeating another Swiss, Fabienne Kocher, to take gold.
Kocher. who beat Chitu in the semi-finals, allowed herself to be turned on the mat and Buchard pounced with a kuzure-kami-shiho-gatame hold for 20 seconds and ippon.
Down at -48kg, last year's world bronze medallist Distria Krasniqi laid down a marker with victory over Olympic champion Paula Pareto.
The Kosovan scored a wazari in the first 10 seconds and almost scored again just before the midway point with a leg sweep.
She was on top throughout the four-minute contest leaving the Argentine with plenty to ponder ahead of Tokyo 2020 although Bilodid will be the gold medal favourite if she decides to drop back to her favoured weight.
Canada's Jessica Klimkait was the class act on judo's comeback in Hungary.
The 2018 Osaka Grand Slam winner cruised through to the final where she needed just 81 seconds to beat France's Helene Receveaux with her fourth ippon out of four on the day.
Klimkait brought up wazari with an over-shoulder throw which she quickly followed up with a 10-second hold to convert the score into a winning ippon.
With just one athlete per country in each weight class, Canada have a real dilemma ahead of Tokyo 2020 with either Klimkait or reigning world champion Crista Deguchi having to miss out.
Two men's classes ended in two all-Russian finals in Budapest.
The -60kg category went to Yago Abuladze who got the better of Robert Mshvidobadze.
Both men were looking for a sacrifice throw and it was Paris Grand Slam runner-up Abduladze who landed it with a minute to go with sumi gaeshi for a wazari score.
At -66kg, Abdula Abdulzhalilov did his Olympic qualifying hopes the power of good with victory over Yakub Shamilov.
When Shamilov missed with an attempted throw, the 29-year-old put him in a tate-shiho-gatame hold and secured it for 20 seconds to score the ippon.