The bobbin case is designed to be removed for cleaning. Take off the needle plate if it is still on the sewing machine. Make sure that the needle and presser foot are fully up. Guide the forked end of the bobbin case under the feed (more or less centered). Then pull the bobbin case under the rim of the position plate. Pull on the side opposite the forked end of the bobbin case. With a small screw driver, turn the lever (at about 10 o'clock on a 12-hour analog clock) towards you. This will lock the bobbin case into place. Make sure that the bobbin case isn't locked too tightly. It still needs to move slightly as the bobbin turns and the needle comes through that plate.
Replace the needle plate and lock it down. Then insert the bobbin and close the slide plate. The manual shows the procedure to remove and replace the bobbin case on the 4562 on page 39. Singer has the manual on the support page: http://www.singerco.com/support/instruction-manuals
. The direct link to the manual is http://www.singerco.com/uploads/download/435_5_8_10_16_22_dial.pdf
I hope this helps.
(I hope that the locking lever hasn't broken. That may require a service person to solve the problem. I'm not entirely sure where that lever is connected to the machine. Some Singer part diagrams are here: http://www.singerco.com/support/replacement-parts-chart . The 4562 may use the same diagram as the 4572, http://parts.singerco.com/CPpartCharts/4_4999/4572.pdf .)