You can probably get away with lag "bolts" (more properly, lag "screws") if you install them properly.
1) Pick a size screw that will pass through the hole in the press's mounting flange, and is about 2-1/2 to 3 inches long.
2) Mock the press into its intended final position and carefully mark the hole positions on the bench. A centering punch is recommended.
3) Remove the press and drill properly sized pilot holes for the screw size and the type of wood involved. Pilot hole size can be derived from any number of fastener guides.
4) Vacuum out the pilot holes.
5) Remount the press. Before installing the screws, dip them in warm or hot water for a second. Drive the screws to the point of contact with the press flange. Then pretty carefully torque the screws to a couple of foot-pounds less than the final torque setting recommended in the fastener guide; do not over torque.
6) After a day or two, re-torque the screws to the recommended final torque setting.
Too big a pilot hole will obviously weaken the screws' engagement; not enough wood to make a firm contact with the thread grooves and lands.
Too small a pilot hole will cause the shaft of the screw to mangle the wood, with the same result.
The water will cause the wood to swell into the thread lands and grooves, making for a better and stronger contact.