When transporting lithium ION batteries on an aircraft the 2017 International rules for transporting them states that the total capacity must not exceed 100Wh. This all applies to all PAX (passenger aircraft) globally. In the US some carriers may allow up to 160Wh. Note that all battery packs / cells must be certified to a UN standard. Here is a snippet of the current regulation as per April 25, 2017:
(18) Except as provided in §173.21 of this subchapter, portable electronic devices (e.g., watches, calculating machines, cameras, cellular phones, laptop and notebook computers, camcorders, medical devices etc.) containing dry cells or dry batteries (including lithium cells or batteries) and spare dry cells or batteries for these devices, when carried by passengers or crew members for personal use. Portable electronic devices powered by lithium batteries may be carried in either checked or carry-on baggage. Spare lithium batteries must be carried in carry-on baggage only. Each installed or spare lithium battery must be of a type proven to meet the requirements of each test in the UN Manual of Tests and Criteria, Part III, Sub-section 38.3 and each spare lithium battery must be individually protected so as to prevent short circuits (e.g., by placement in original retail packaging, by otherwise insulating terminals by taping over exposed terminals, or placing each battery in a separate plastic bag or protective pouch). In addition, each installed or spare lithium battery must not exceed the following:
(i) For a lithium metal battery, a lithium content of not more than 2 grams per battery; or
(ii) For a lithium ion battery, the Watt-hour rating must not exceed 100 Wh. With the approval of the operator, portable electronic devices may contain lithium ion batteries exceeding 100 Wh, but not exceeding 160 Wh and no more than two individually protected lithium ion batteries each exceeding 100 Wh, but not exceeding 160 Wh, may be carried per person as spare batteries in carry-on baggage.
(iii) For a non-spillable battery, the battery and equipment must conform to §173.159a(d). Each battery must not exceed a voltage greater than 12 volts and a watt-hour rating of not more than 100 Wh. No more than two individually protected spare batteries may be carried. Such equipment and spare batteries must be carried in checked or carry-on baggage.
(iv) Articles containing lithium metal or lithium ion cells or batteries the primary purpose of which is to provide power to another device must be carried as spare batteries in accordance with the provisions of this paragraph.
Shipping lithium ION batteries such as the size and capacity found on most electric bicycles whether they are shipped on their own or contained within equipment need to identified as such. This falls under Class 9 Dangerous goods and regardless if shipped by Air or Ground require that they be packed and labeled in compliance by a trained and certified shipper. Shipping by ground is easier compared to air. Shipping by air requires very specific packing instructions, packing materials and that the shipper be certified.