Because BUG decks play so many efficient, value-oriented threats, you will probably want to be on the Marit Lage plan as early as is a sure kill, but if you can achieve it, Wasteland and Life from the Loam is often the best way ensure that threats never land.
Shardless is a deck that relies on casting spells at 3 CMC or higher for best value, and if you can keep them at or under 2 mana, you will remove most advantage that they might gain from Ancestral Vision or Shardless Agent. Other BUG decks rely on Snapcaster Mage and Baleful Strix/Hymn to Tourach to drive value, eventually finishing with tiny beats or Jace, the Mind Sculptor, Gurmag Angler (or Tombstalker.)
Shardless decks do not play too many counterspells (some lists running only three Force of Will maindeck), so unless you have knowledge of your opponent’s hand, and you know they have a counterspell, cast your threats as if they do not – you are more likely to see Hymn to Tourach or Thoughtseize. BUG Control decks may run more straight Counterspell and attempt to use them with Snapcaster Mage, so attack the mana-base and play your spells a little more carefully to bait counter-magic before landing more powerful threats.
When sideboarding, remove all countermagic. Bring in all sweepers, planeswalkers, and removal. Plan for a very long, grindy game — recommend not over-committing to Crop Rotation and including at most 3 post-sideboard.
Bring in any card that has potential for a two-for-one trade, including Golgari Charm if you have room, as this can sometimes remove Baleful Strix as a blocker for Marit Lage (making it difficult to swing in while they have access to their own Liliana of the Veil or Jace, The Mind Sculptor.