Dialga G and Gengar prolly give Speedrill the hardest time...
Dialga G just T1 Deafen and don't stop. Toss Galactic HQ out and by the time all 4 Beedrills are out they should be pretty beat up. Toss Power Sprays at them and by the time they're set up you should be able to run them through, because HQ + Deafen + Poison really adds up across the field. Most Dialgas play Palkia for fire matches anyways, so if you can get it up while keeping the Deafen lock you can cause some harm. Palkia G + Mesprit lock also usually plays Dialga G to shut off a few unfavorable Bodies (Mewtwo, Nidoqueen, etc.), so if you play that you can do close to the same method. Without Dialga G, or if you perform sloppy Deafen lock, the match up gets much harder... most Beedrills can manage with just the 4 Bees (Night maintenane is pretty much all they need to bounce back, and you're not exactly trading prizes), and drop a Baltoy to BTS up to Claydol or an Uxie when they start to get dead hands then toss it to the lost zone. Power lock kills it, yeah, but I hardly see that as an "autowin" 'cuz the Mesprit lock, in theory, kills everything... yet few will claim Palkia + Mesprit lock as BDIF. Besides, I saw a few Beedrills playing Mesprits of their own.
Gengar gives it a tough time too, I personally played 3 in Swiss at Nats and had no problem. T1 Pitch-Dark really slows them down, usually jumping to a T2 KO with Poltergiest. If Bees jump out, hit a benched Flutter Wings for 60, take a KO and hope to trade prizes, then finish the other off with a new Gengar. If the Gengar plays Mesprits, it helps tons.