Keeping count is recommended for mantra-recitation, and not for meditation. Herein, the count acts as an offering to the deity, and thus if using the fingers for counting, we face them palm-upwards as an offering, or the rosary is held up high at the height of our heart, as an offering. In case of a rosary, it may not touch the ground or legs/feet, and is at best kept in a pouch or bag to hide the offering from all but one’s personal deity. Thus the covering or bag is meant to hide the rosary from anyone but one’s deity whom one keeps as secret as the rosary. The implication of this is also that worship is best done in secret.
If you know how to use the ‘kāramāla’, or counting with fingers, then it is recommended to learn. This is a specific method also taught in the book Mantra Yoga Samhita:

Top hand is for male deity worship, and the bottom is for female. Left-image is for counting the first hundred, and right-image is for the remaining eight, to complete 108. The right hand is used for this, as the left is used to keep count of the right.
If counting with fingers is too confusing, rosaries are recommended.
- Guru is worshipped with all types of rosaries, but Haldi (turmeric) is specific to the Guru. This is also recommended for Hanuman worship.
- Rudrākṣa Rosary is for Śiva and Gaṇeśa. Gaṇeśa is also worshipped with Red Coral or gemstones.
- Pravala or Rakta Chandan (red sandalwood) is for Sūrya and Gayatri.
- Tulsi is for Viṣṇu and Lakṣmī. Black Tulsi is specific to Kṛṣṇa.
- Śakti is worshipped with a variety of rosary, but pearl and Spatik (rock-crystal) is specific to her, as is Śveta Chandan (white sandalwood). Komala (lotus-seed) is also popular but difficult to maintain. This is recommended for those seeking to marry. Sarasvatī is also worshipped with Spatik.
Under no circumstances are rosaries made of human or animal bones recommended for worship.